09 September 2021 10:12:36.025 AM ELLIPTIC_INTEGRAL_TEST(): FORTRAN90 version ELLIPTIC_INTEGRAL() evaluates elliptic integral functions using Carlson's elliptic functions. RC_TEST RC evaluates the elementary integral RC(X,Y) X Y RC(X,Y) 0.1510000000000000D-77 0.1510000000000000D-77 0.8137884587711593D+39 0.3010000000000000D-77 0.5500000000000000D-78 0.9524521540989471D+39 0.0000000000000000D+00 0.3010000000000000D-77 0.9053919509295885D+39 0.9900000000000000D+75 0.5500000000000000D-78 0.5629713505821428D-35 0.0000000000000000D+00 0.9900000000000000D+75 0.4992318443077758D-37 0.9900000000000000D+75 0.9900000000000000D+75 0.3178208630818641D-37 RC - Error! Invalid input arguments. X = 0.0000000000000000D+00 Y = 0.2000000000000000D-77 0.0000000000000000D+00 0.2000000000000000D-77 ***Error*** 0.0000000000000000D+00 0.2500000000000000D+00 0.3141592653589793D+01 0.6250000000000000D-01 0.1250000000000000D+00 0.3141592653589793D+01 0.2250000000000000D+01 0.2000000000000000D+01 0.6931471805599454D+00 0.1000000000000000D-01 0.1000000000000000D+01 0.1478037662374775D+01 0.2000000000000000D-01 0.1000000000000000D+01 0.1443406235712271D+01 0.5000000000000000D-01 0.1000000000000000D+01 0.1380231154269966D+01 0.1000000000000000D+00 0.1000000000000000D+01 0.1316609847527586D+01 0.2000000000000000D+00 0.1000000000000000D+01 0.1237829897094659D+01 0.4000000000000000D+00 0.1000000000000000D+01 0.1143920647968054D+01 0.6000000000000000D+00 0.1000000000000000D+01 0.1082636119571208D+01 0.8000000000000000D+00 0.1000000000000000D+01 0.1036747571331046D+01 0.1000000000000000D+01 0.1000000000000000D+01 0.1000000000000000D+01 0.1200000000000000D+01 0.1000000000000000D+01 0.9693519329631458D+00 0.1500000000000000D+01 0.1000000000000000D+01 0.9312298594527122D+00 0.2000000000000000D+01 0.1000000000000000D+01 0.8813735870195432D+00 0.3000000000000000D+01 0.1000000000000000D+01 0.8104969894767539D+00 0.4000000000000000D+01 0.1000000000000000D+01 0.7603459963009465D+00 0.5000000000000000D+01 0.1000000000000000D+01 0.7218177375894052D+00 0.1000000000000000D+02 0.1000000000000000D+01 0.6061488197440222D+00 0.2000000000000000D+02 0.1000000000000000D+01 0.4997299176960261D+00 0.5000000000000000D+02 0.1000000000000000D+01 0.3777315372940898D+00 0.1000000000000000D+03 0.1000000000000000D+01 0.3008302149854818D+00 0.1000000000000000D+04 0.1000000000000000D+01 0.1311981462667840D+00 0.1000000000000000D+05 0.1000000000000000D+01 0.5298557300099017D-01 0.1000000000000000D+06 0.1000000000000000D+01 0.2039555141711115D-01 0.1000000000000000D+07 0.1000000000000000D+01 0.7600906009995943D-02 0.1000000000000000D+08 0.1000000000000000D+01 0.2767687204982141D-02 0.1000000000000000D+09 0.1000000000000000D+01 0.9903487599553565D-03 0.1000000000000000D+10 0.1000000000000000D+01 0.3495828416193509D-03 0.1000000000000000D+11 0.1000000000000000D+01 0.1220607264611548D-03 0.1000000000000000D+13 0.1000000000000000D+01 0.1450865773853122D-04 0.1000000000000000D+16 0.1000000000000000D+01 0.5680252434588194D-06 0.1000000000000000D+21 0.1000000000000000D+01 0.2371899811050040D-08 0.1000000000000000D+31 0.1000000000000000D+01 0.3523192357547063D-13 0.1000000000000000D+41 0.1000000000000000D+01 0.4674484904044085D-18 0.1000000000000000D+51 0.1000000000000000D+01 0.5825777450541109D-23 RC_TEST2 Compare LOG(X)/(X-1) and ARCTAN(X) with values based on RC. X From LOG From RC 0.2D+00 0.2011797390542625D+01 0.2011797390542625D+01 0.4D+00 0.1527151219790258D+01 0.1527151219790258D+01 0.6D+00 0.1277064059414976D+01 0.1277064059414977D+01 0.8D+00 0.1115717756571049D+01 0.1115717756571049D+01 0.1D+01 **** ZERO DIVIDE ***** 0.1000000000000000D+01 0.1D+01 0.9116077839697732D+00 0.9116077839697730D+00 0.1D+01 0.8411805915530323D+00 0.8411805915530324D+00 0.2D+01 0.7833393820762259D+00 0.7833393820762258D+00 0.2D+01 0.7347333311276488D+00 0.7347333311276486D+00 0.2D+01 0.6931471805599453D+00 0.6931471805599454D+00 Extreme values of X X From LOG From RC 0.1D-74 0.1726938819745534D+03 0.1726938819745534D+03 0.1D-64 0.1496680310446130D+03 0.1496680310446130D+03 0.1D-54 0.1266421801146725D+03 0.1266421801146725D+03 0.1D-44 0.1036163291847321D+03 0.1036163291847320D+03 0.1D-34 0.8059047825479161D+02 0.8059047825479161D+02 0.1D-24 0.5756462732485114D+02 0.5756462732485113D+02 0.1D-14 0.3453877639491072D+02 0.3453877639491072D+02 0.1D-04 0.1151304059537618D+02 0.1151304059537618D+02 0.1D+06 0.1151304059537618D-03 0.1151304059537618D-03 0.1D+16 0.3453877639491072D-13 0.3453877639491072D-13 0.1D+26 0.5756462732485114D-23 0.5756462732485114D-23 0.1D+36 0.8059047825479162D-33 0.8059047825479158D-33 0.1D+46 0.1036163291847320D-42 0.1036163291847321D-42 0.1D+56 0.1266421801146725D-52 0.1266421801146725D-52 0.1D+66 0.1496680310446129D-62 0.1496680310446130D-62 0.1D+76 0.1726938819745534D-72 0.1726938819745534D-72 X From ARCTAN From RC RC - Error! Invalid input arguments. X = 0.1000000000000000D+76 Y = 0.1000000000000000D+76 0.1D-74 0.1000000000000000D-74 0.0000000000000000D+00 0.1D-14 0.1000000000000000D-14 0.9999999999999999D-15 0.1D-02 0.9999996666668668D-03 0.9999996666668666D-03 0.1D+00 0.9966865249116204D-01 0.9966865249116202D-01 0.2D+00 0.1973955598498808D+00 0.1973955598498808D+00 0.5D+00 0.4636476090008061D+00 0.4636476090008061D+00 0.1D+01 0.7853981633974483D+00 0.7853981633974482D+00 0.2D+01 0.1107148717794090D+01 0.1107148717794091D+01 0.5D+01 0.1373400766945016D+01 0.1373400766945016D+01 0.1D+02 0.1471127674303735D+01 0.1471127674303734D+01 0.1D+04 0.1569796327128230D+01 0.1569796327128230D+01 0.1D+16 0.1570796326794896D+01 0.1570796326794896D+01 0.1D+76 0.1570796326794897D+01 0.1570796326794897D+01 RD_TEST RD evaluates the Carlson elliptic integral of the second kind, RD(X,Y,Z) X Y Z RD(X,Y,Z) 0.0000000000000000D+00 0.6010000000000001D-50 0.6010000000000001D-50 0.5057075390167092D+76 0.5500000000000000D-78 0.6010000000000001D-50 0.6010000000000001D-50 0.5057075390167032D+76 0.0000000000000000D+00 0.6010000000000001D-50 0.9900000000000000D+48 0.3455579458524223D-69 0.5500000000000000D-78 0.6010000000000001D-50 0.9900000000000000D+48 0.3455579458524223D-69 0.0000000000000000D+00 0.9900000000000000D+48 0.6010000000000001D-50 0.5016827696801392D+27 0.5500000000000000D-78 0.9900000000000000D+48 0.6010000000000001D-50 0.5016827696801343D+27 0.0000000000000000D+00 0.9900000000000000D+48 0.9900000000000000D+48 0.2391984406816877D-71 0.5500000000000000D-78 0.9900000000000000D+48 0.9900000000000000D+48 0.2391984406816877D-71 0.3010000000000000D-50 0.3010000000000000D-50 0.6010000000000001D-50 0.3170935022408316D+76 0.3010000000000000D-50 0.3010000000000000D-50 0.9900000000000000D+48 0.3444999003763636D-69 0.9900000000000000D+48 0.9900000000000000D+48 0.6010000000000001D-50 0.3908848372573853D-22 0.9900000000000000D+48 0.9900000000000000D+48 0.9900000000000000D+48 0.1015189712383042D-71 RD - Error! Invalid input arguments. X = 0.0000000000000000D+00 Y = 0.3010000000000000D-50 Z = 0.1000000000000000D+01 0.0000000000000000D+00 0.3010000000000000D-50 0.1000000000000000D+01 ***Error*** 0.0000000000000000D+00 0.2000000000000000D+01 0.1000000000000000D+01 0.1797210352103389D+01 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D-09 0.4242559649759194D+06 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D-04 0.1333576985789446D+04 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D-01 0.3543137955816859D+02 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D+00 0.8049184457709792D+01 0.5000000000000000D+00 0.1000000000000000D+01 0.2000000000000000D+00 0.4795496764410121D+01 0.5000000000000000D+00 0.1000000000000000D+01 0.5000000000000000D+00 0.2260648559158617D+01 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D+01 0.1210841860059132D+01 0.5000000000000000D+00 0.1000000000000000D+01 0.2000000000000000D+01 0.6176739675072550D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.5000000000000000D+01 0.2361769958541499D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D+02 0.1086719981146340D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D+03 0.6540379849123936D-02 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D+06 0.5320236560151541D-06 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D+11 0.3409325949193374D-13 RF_TEST RF evaluates the Carlson elliptic integral of the first kind, RF(X,Y,Z) X Y Z RF(X,Y,Z) 0.1510000000000000D-77 0.1510000000000000D-77 0.1510000000000000D-77 0.8137884587711593D+39 0.1510000000000000D-77 0.1510000000000000D-77 0.9900000000000000D+75 0.5613664399997798D-35 0.0000000000000000D+00 0.3010000000000000D-77 0.3010000000000000D-77 0.9053919509295885D+39 0.0000000000000000D+00 0.3010000000000000D-77 0.9900000000000000D+75 0.5624731938415326D-35 0.0000000000000000D+00 0.9900000000000000D+75 0.9900000000000000D+75 0.4992318443077759D-37 0.9900000000000000D+75 0.9900000000000000D+75 0.9900000000000000D+75 0.3178208630818641D-37 0.5500000000000000D-78 0.3010000000000000D-77 0.3010000000000000D-77 0.7198956468812792D+39 0.5500000000000000D-78 0.3010000000000000D-77 0.9900000000000000D+75 0.5613420743331975D-35 0.5500000000000000D-78 0.9900000000000000D+75 0.9900000000000000D+75 0.4992318443077759D-37 RF - Error! Invalid input arguments. X = 0.0000000000000000D+00 Y = 0.2000000000000000D-77 Z = 0.1000000000000000D+01 0.0000000000000000D+00 0.2000000000000000D-77 0.1000000000000000D+01 ***Error*** 0.0000000000000000D+00 0.1000000000000000D+01 0.2000000000000000D+01 0.1311028777146060D+01 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D+01 0.1110720734539592D+01 0.5000000000000000D+00 0.1000000000000000D+01 0.1100000000000000D+01 0.1091430716268119D+01 0.5000000000000000D+00 0.1000000000000000D+01 0.1200000000000000D+01 0.1073732561377385D+01 0.5000000000000000D+00 0.1000000000000000D+01 0.1300000000000000D+01 0.1057389655801202D+01 0.5000000000000000D+00 0.1000000000000000D+01 0.1400000000000000D+01 0.1042214695930046D+01 0.5000000000000000D+00 0.1000000000000000D+01 0.1500000000000000D+01 0.1028056801052127D+01 0.5000000000000000D+00 0.1000000000000000D+01 0.1600000000000000D+01 0.1014792597551546D+01 0.5000000000000000D+00 0.1000000000000000D+01 0.1700000000000000D+01 0.1002319885847406D+01 0.5000000000000000D+00 0.1000000000000000D+01 0.1800000000000000D+01 0.9905530382414446D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.1900000000000000D+01 0.9794195874708435D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.2000000000000000D+01 0.9688576532724523D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.2200000000000000D+01 0.9492423586314841D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.2400000000000000D+01 0.9313590566024380D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.2600000000000000D+01 0.9149398964447096D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.2800000000000000D+01 0.8997743463505848D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.3000000000000000D+01 0.8856939232035483D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.3500000000000000D+01 0.8543997654075564D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.4000000000000000D+01 0.8275182379903345D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.4500000000000000D+01 0.8040168167992912D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.5000000000000000D+01 0.7831840398091505D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.6000000000000000D+01 0.7476135036481746D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.7000000000000000D+01 0.7180694683312081D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.8000000000000000D+01 0.6929108826625124D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.9000000000000000D+01 0.6710782484938838D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D+02 0.6518490214136576D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.2000000000000000D+02 0.5331872892861481D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.3000000000000000D+02 0.4706527717638377D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.4000000000000000D+02 0.4295233682160168D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.5000000000000000D+02 0.3994861473220863D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D+03 0.3163981445460594D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.2000000000000000D+03 0.2479287246742144D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.5000000000000000D+03 0.1771580322263678D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D+04 0.1361926299714245D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D+05 0.5456849363690315D-01 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D+06 0.2089626719954944D-01 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D+07 0.7759252354859355D-02 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D+09 0.1006183477210615D-02 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D+11 0.1236441982979439D-03 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D+13 0.1466700492234990D-04 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D+16 0.5730326210782770D-06 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D+21 0.2387734529432078D-08 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D+31 0.3539027075929101D-13 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D+41 0.4690319622426123D-18 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D+51 0.5841612168923146D-23 RJ_TEST RJ evaluates the Carlson elliptic integral of the third kind, RJ(X,Y,Z,P) X Y Z P RJ(X,Y,Z,P) 0.1010000000000000D-25 0.1010000000000000D-25 0.1010000000000000D-25 0.2010000000000000D-25 0.6363797977910284D+39 0.1010000000000000D-25 0.1010000000000000D-25 0.2990000000000000D+25 0.2010000000000000D-25 0.5969809640810398D+14 0.0000000000000000D+00 0.2010000000000000D-25 0.2010000000000000D-25 0.2010000000000000D-25 0.8268315690384853D+39 0.0000000000000000D+00 0.2010000000000000D-25 0.2990000000000000D+25 0.2010000000000000D-25 0.8631566148749853D+14 0.0000000000000000D+00 0.2990000000000000D+25 0.2990000000000000D+25 0.2010000000000000D-25 0.1111659835295890D-10 0.2990000000000000D+25 0.2990000000000000D+25 0.2990000000000000D+25 0.2010000000000000D-25 0.3333899154957826D-34 0.5500000000000000D-78 0.2010000000000000D-25 0.2010000000000000D-25 0.2010000000000000D-25 0.8268315690384853D+39 0.5500000000000000D-78 0.2010000000000000D-25 0.2990000000000000D+25 0.2010000000000000D-25 0.8631566148749853D+14 0.5500000000000000D-78 0.2990000000000000D+25 0.2990000000000000D+25 0.2010000000000000D-25 0.1111659835295890D-10 0.2010000000000000D-25 0.2010000000000000D-25 0.2010000000000000D-25 0.2010000000000000D-25 0.3509182168450738D+39 0.1010000000000000D-25 0.1010000000000000D-25 0.1010000000000000D-25 0.2990000000000000D+25 0.9983650737892871D-11 0.1010000000000000D-25 0.1010000000000000D-25 0.2990000000000000D+25 0.2990000000000000D+25 0.3353865073488965D-34 0.0000000000000000D+00 0.2010000000000000D-25 0.2010000000000000D-25 0.2990000000000000D+25 0.1111659835295890D-10 0.0000000000000000D+00 0.2010000000000000D-25 0.2990000000000000D+25 0.2990000000000000D+25 0.3374118957422856D-34 0.0000000000000000D+00 0.2990000000000000D+25 0.2990000000000000D+25 0.2990000000000000D+25 0.4557265740116441D-36 0.2990000000000000D+25 0.2990000000000000D+25 0.2990000000000000D+25 0.2990000000000000D+25 0.1934163652061004D-36 0.5500000000000000D-78 0.2010000000000000D-25 0.2010000000000000D-25 0.2990000000000000D+25 0.1111659835295890D-10 0.5500000000000000D-78 0.2010000000000000D-25 0.2990000000000000D+25 0.2990000000000000D+25 0.3374118957422856D-34 0.5500000000000000D-78 0.2990000000000000D+25 0.2990000000000000D+25 0.2990000000000000D+25 0.4557265740116441D-36 0.2010000000000000D-25 0.2010000000000000D-25 0.2010000000000000D-25 0.2990000000000000D+25 0.7077046312962523D-11 RJ - Error! Invalid input arguments. X = 0.0000000000000000D+00 Y = 0.1900000000000000D-25 Z = 0.1900000000000000D-25 P = 0.1000000000000000D+01 0.0000000000000000D+00 0.1900000000000000D-25 0.1900000000000000D-25 0.1000000000000000D+01 ***Error*** 0.2000000000000000D+01 0.3000000000000000D+01 0.4000000000000000D+01 0.5000000000000000D+01 0.1429757966715675D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D+01 0.2500000000000000D+00 0.2608105757997978D+01 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D+01 0.7500000000000000D+00 0.1442864193614197D+01 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D+01 0.1000000000000000D+01 0.1210841860059132D+01 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D+01 0.2000000000000000D+01 0.7670625432950464D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.2000000000000000D+01 0.2500000000000000D+00 0.2008380291058661D+01 0.5000000000000000D+00 0.1000000000000000D+01 0.2000000000000000D+01 0.7500000000000000D+00 0.1136845217951276D+01 0.5000000000000000D+00 0.1000000000000000D+01 0.2000000000000000D+01 0.1500000000000000D+01 0.7460643441600711D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.2000000000000000D+01 0.4000000000000000D+01 0.3794195060366037D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.5000000000000000D+01 0.2500000000000000D+00 0.1370892718222587D+01 0.5000000000000000D+00 0.1000000000000000D+01 0.5000000000000000D+01 0.7500000000000000D+00 0.7949204422899481D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.5000000000000000D+01 0.3000000000000000D+01 0.3385294211417840D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.5000000000000000D+01 0.1000000000000000D+02 0.1398476510985250D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D+02 0.2500000000000000D+00 0.1005572682199914D+01 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D+02 0.7500000000000000D+00 0.5908850286211613D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D+02 0.5000000000000000D+01 0.1811791604390096D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D+02 0.2000000000000000D+02 0.6283564851298871D-01 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D+03 0.2500000000000000D+00 0.3343272158567165D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D+03 0.7500000000000000D+00 0.2006464395741285D+00 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D+03 0.5000000000000000D+02 0.1167793209710091D-01 0.5000000000000000D+00 0.1000000000000000D+01 0.1000000000000000D+03 0.2000000000000000D+03 0.3581148146400939D-02 ELLIPTIC_FA_TEST: ELLIPTIC_FA returns values of the complete elliptic integral of the first kind, with parameter angle A. A F(A) F(A) Tabulated Calculated 0.000000 1.570796326794897 1.570796326794897 5.000000 1.573792130924768 1.573792130924768 10.000000 1.582842804338351 1.582842804338351 15.000000 1.598142002112540 1.598142002112540 20.000000 1.620025899124204 1.620025899124204 25.000000 1.648995218478530 1.648995218478531 30.000000 1.685750354812596 1.685750354812596 35.000000 1.731245175657058 1.731245175657058 40.000000 1.786769134885021 1.786769134885021 45.000000 1.854074677301372 1.854074677301372 50.000000 1.935581096004722 1.935581096004722 55.000000 2.034715312185791 2.034715312185790 60.000000 2.156515647499643 2.156515647499643 65.000000 2.308786798167196 2.308786798167196 70.000000 2.504550079001634 2.504550079001633 75.000000 2.768063145368768 2.768063145368768 80.000000 3.153385251887839 3.153385251887837 85.000000 3.831741999784146 3.831741999784148 ELLIPTIC_FK_TEST: ELLIPTIC_FK returns values of the complete elliptic integral of the first kind, with parameter K. K F(K) F(K) Tabulated Calculated 0.000000 1.570796326794897 1.570796326794897 0.223607 1.591003453790792 1.591003453790792 0.316228 1.612441348720219 1.612441348720219 0.387298 1.635256732264580 1.635256732264580 0.447214 1.659623598610528 1.659623598610528 0.500000 1.685750354812596 1.685750354812596 0.547723 1.713889448178791 1.713889448178791 0.591608 1.744350597225613 1.744350597225613 0.632456 1.777519371491253 1.777519371491253 0.670820 1.813883936816983 1.813883936816982 0.707107 1.854074677301372 1.854074677301372 0.741620 1.898924910271554 1.898924910271553 0.774597 1.949567749806026 1.949567749806026 0.806226 2.007598398424376 2.007598398424376 0.836660 2.075363135292469 2.075363135292470 0.866025 2.156515647499643 2.156515647499643 0.894427 2.257205326820854 2.257205326820854 0.921954 2.389016486325580 2.389016486325581 0.948683 2.578092113348173 2.578092113348173 0.974679 2.908337248444552 2.908337248444551 ELLIPTIC_FM_TEST: ELLIPTIC_FM returns values of the complete elliptic integral of the first kind, with parameter M. M F(M) F(M) Tabulated Calculated 0.000000 1.570796326794897 1.570796326794897 0.050000 1.591003453790792 1.591003453790793 0.100000 1.612441348720219 1.612441348720220 0.150000 1.635256732264580 1.635256732264580 0.200000 1.659623598610528 1.659623598610528 0.250000 1.685750354812596 1.685750354812596 0.300000 1.713889448178791 1.713889448178791 0.350000 1.744350597225613 1.744350597225613 0.400000 1.777519371491253 1.777519371491253 0.450000 1.813883936816983 1.813883936816982 0.500000 1.854074677301372 1.854074677301372 0.550000 1.898924910271554 1.898924910271553 0.600000 1.949567749806026 1.949567749806026 0.650000 2.007598398424376 2.007598398424376 0.700000 2.075363135292469 2.075363135292469 0.750000 2.156515647499643 2.156515647499643 0.800000 2.257205326820854 2.257205326820854 0.850000 2.389016486325580 2.389016486325580 0.900000 2.578092113348173 2.578092113348173 0.950000 2.908337248444552 2.908337248444551 ELLIPTIC_EA_TEST: ELLIPTIC_EA returns values of the complete elliptic integral of the second kind, with parameter angle A. A E(A) E(A) Tabulated Calculated 0.000000 1.570796326794897 1.570796326794897 5.000000 1.567809073977622 1.567809073977621 10.000000 1.558887196601596 1.558887196601596 15.000000 1.544150496914673 1.544150496914673 20.000000 1.523799205259774 1.523799205259774 25.000000 1.498114928422116 1.498114928422115 30.000000 1.467462209339427 1.467462209339427 35.000000 1.432290969306756 1.432290969306756 40.000000 1.393140248523812 1.393140248523812 45.000000 1.350643881047676 1.350643881047676 50.000000 1.305539094297794 1.305539094297794 55.000000 1.258679624779997 1.258679624779997 60.000000 1.211056027568459 1.211056027568460 65.000000 1.163827964493139 1.163827964493139 70.000000 1.118377737969864 1.118377737969863 75.000000 1.076405113076403 1.076405113076403 80.000000 1.040114395706010 1.040114395706010 85.000000 1.012663506234396 1.012663506234396 RF - Error! Invalid input arguments. X = 0.0000000000000000D+00 Y = 0.0000000000000000D+00 Z = 0.1000000000000000D+01 RD - Error! Invalid input arguments. X = 0.0000000000000000D+00 Y = 0.0000000000000000D+00 Z = 0.1000000000000000D+01 90.000000 1.000000000000000 0.000000000000000 ELLIPTIC_EK_TEST: ELLIPTIC_EK returns values of the complete elliptic integral of the second kind, with parameter K. K E(K) E(K) Tabulated Calculated 0.000000 1.570796326794897 1.570796326794897 0.223607 1.550973351780472 1.550973351780472 0.316228 1.530757636897763 1.530757636897763 0.387298 1.510121832092819 1.510121832092819 0.447214 1.489035058095853 1.489035058095853 0.500000 1.467462209339427 1.467462209339427 0.547723 1.445363064412665 1.445363064412665 0.591608 1.422691133490879 1.422691133490879 0.632456 1.399392138897432 1.399392138897432 0.670820 1.375401971871116 1.375401971871116 0.707107 1.350643881047676 1.350643881047676 0.741620 1.325024497958230 1.325024497958230 0.774597 1.298428035046913 1.298428035046913 0.806226 1.270707479650149 1.270707479650150 0.836660 1.241670567945823 1.241670567945823 0.866025 1.211056027568459 1.211056027568460 0.894427 1.178489924327839 1.178489924327839 0.921954 1.143395791883166 1.143395791883166 0.948683 1.104774732704073 1.104774732704073 0.974679 1.060473727766278 1.060473727766278 RF - Error! Invalid input arguments. X = 0.0000000000000000D+00 Y = 0.0000000000000000D+00 Z = 0.1000000000000000D+01 RD - Error! Invalid input arguments. X = 0.0000000000000000D+00 Y = 0.0000000000000000D+00 Z = 0.1000000000000000D+01 1.000000 1.000000000000000 0.000000000000000 ELLIPTIC_EM_TEST: ELLIPTIC_EM returns values of the complete elliptic integral of the second kind, with parameter M. M E(M) E(M) Tabulated Calculated 0.000000 1.570796326794897 1.570796326794897 0.050000 1.550973351780472 1.550973351780473 0.100000 1.530757636897763 1.530757636897763 0.150000 1.510121832092819 1.510121832092819 0.200000 1.489035058095853 1.489035058095852 0.250000 1.467462209339427 1.467462209339427 0.300000 1.445363064412665 1.445363064412665 0.350000 1.422691133490879 1.422691133490879 0.400000 1.399392138897432 1.399392138897432 0.450000 1.375401971871116 1.375401971871116 0.500000 1.350643881047676 1.350643881047676 0.550000 1.325024497958230 1.325024497958230 0.600000 1.298428035046913 1.298428035046913 0.650000 1.270707479650149 1.270707479650149 0.700000 1.241670567945823 1.241670567945823 0.750000 1.211056027568459 1.211056027568460 0.800000 1.178489924327839 1.178489924327839 0.850000 1.143395791883166 1.143395791883166 0.900000 1.104774732704073 1.104774732704073 0.950000 1.060473727766278 1.060473727766278 RF - Error! Invalid input arguments. X = 0.0000000000000000D+00 Y = 0.0000000000000000D+00 Z = 0.1000000000000000D+01 RD - Error! Invalid input arguments. X = 0.0000000000000000D+00 Y = 0.0000000000000000D+00 Z = 0.1000000000000000D+01 1.000000 1.000000000000000 0.000000000000000 ELLIPTIC_PIA_TEST: ELLIPTIC_PIA returns values of the complete elliptic integral of the third kind, with parameter angle A. N A Pi(N,A) Pi(N,A) Tabulated Calculated -10.000000 30.000000 0.4892245275965397 0.4892245275965397 -10.000000 45.000000 0.5106765677902629 0.5106765677902629 -10.000000 60.000000 0.5460409271920561 0.5460409271920565 -10.000000 77.079034 0.6237325893535237 0.6237325893535237 -3.000000 30.000000 0.8230455426606750 0.8230455426606752 -3.000000 45.000000 0.8760028274011437 0.8760028274011439 -3.000000 60.000000 0.9660073560143946 0.9660073560143951 -3.000000 77.079034 1.171952391481798 1.171952391481798 -1.000000 30.000000 1.177446843000566 1.177446843000566 -1.000000 45.000000 1.273127366749682 1.273127366749682 -1.000000 60.000000 1.440034318657551 1.440034318657551 -1.000000 77.079034 1.836472172302591 1.836472172302590 0.000000 30.000000 1.685750354812596 1.685750354812596 0.000000 45.000000 1.854074677301372 1.854074677301372 0.000000 60.000000 2.156515647499643 2.156515647499643 0.000000 77.079034 2.908337248444552 2.908337248444551 0.500000 30.000000 2.413671504201195 2.413671504201195 0.500000 45.000000 2.701287762095351 2.701287762095351 0.500000 60.000000 3.234773471249465 3.234773471249465 0.500000 77.079034 4.633308147279891 4.633308147279889 ELLIPTIC_PIK_TEST: ELLIPTIC_PIK returns values of the complete elliptic integral of the third kind, with parameter K. N K Pi(N,K) Pi(N,K) Tabulated Calculated -10.000000 0.500000 0.4892245275965397 0.4892245275965397 -10.000000 0.707107 0.5106765677902629 0.5106765677902632 -10.000000 0.866025 0.5460409271920561 0.5460409271920565 -10.000000 0.974679 0.6237325893535237 0.6237325893535237 -3.000000 0.500000 0.8230455426606750 0.8230455426606752 -3.000000 0.707107 0.8760028274011437 0.8760028274011439 -3.000000 0.866025 0.9660073560143946 0.9660073560143951 -3.000000 0.974679 1.171952391481798 1.171952391481798 -1.000000 0.500000 1.177446843000566 1.177446843000566 -1.000000 0.707107 1.273127366749682 1.273127366749683 -1.000000 0.866025 1.440034318657551 1.440034318657551 -1.000000 0.974679 1.836472172302591 1.836472172302590 0.000000 0.500000 1.685750354812596 1.685750354812596 0.000000 0.707107 1.854074677301372 1.854074677301372 0.000000 0.866025 2.156515647499643 2.156515647499643 0.000000 0.974679 2.908337248444552 2.908337248444551 0.500000 0.500000 2.413671504201195 2.413671504201195 0.500000 0.707107 2.701287762095351 2.701287762095351 0.500000 0.866025 3.234773471249465 3.234773471249465 0.500000 0.974679 4.633308147279891 4.633308147279889 ELLIPTIC_PIM_TEST: ELLIPTIC_PIM returns values of the complete elliptic integral of the third kind, with parameter modulus M. N M Pi(N,M) Pi(N,M) Tabulated Calculated -10.000000 0.250000 0.4892245275965397 0.4892245275965397 -10.000000 0.500000 0.5106765677902629 0.5106765677902629 -10.000000 0.750000 0.5460409271920561 0.5460409271920565 -10.000000 0.950000 0.6237325893535237 0.6237325893535228 -3.000000 0.250000 0.8230455426606750 0.8230455426606752 -3.000000 0.500000 0.8760028274011437 0.8760028274011439 -3.000000 0.750000 0.9660073560143946 0.9660073560143951 -3.000000 0.950000 1.171952391481798 1.171952391481798 -1.000000 0.250000 1.177446843000566 1.177446843000566 -1.000000 0.500000 1.273127366749682 1.273127366749682 -1.000000 0.750000 1.440034318657551 1.440034318657551 -1.000000 0.950000 1.836472172302591 1.836472172302590 0.000000 0.250000 1.685750354812596 1.685750354812596 0.000000 0.500000 1.854074677301372 1.854074677301372 0.000000 0.750000 2.156515647499643 2.156515647499643 0.000000 0.950000 2.908337248444552 2.908337248444551 0.500000 0.250000 2.413671504201195 2.413671504201195 0.500000 0.500000 2.701287762095351 2.701287762095351 0.500000 0.750000 3.234773471249465 3.234773471249465 0.500000 0.950000 4.633308147279891 4.633308147279889 ELLIPTIC_INC_FA_TEST: ELLIPTIC_INC_FA returns values of the incomplete elliptic integral of the first kind, with parameters PHI, A. PHI A F(PHI,A) F(PHI,A) Tabulated Calculated 0.343091 123.082123 0.3478806460316299 0.3478806460316299 1.302990 11.269317 1.313180577009584 1.313180577009584 0.652363 -94.888065 0.7037956689264326 0.7037956689264325 0.404602 -99.714079 0.4157626844675118 0.4157626844675119 0.068846 57.058810 0.6888475483285136E-01 0.6888475483285136E-01 0.096961 -19.713633 0.9697816754845832E-01 0.9697816754845830E-01 0.630370 56.312303 0.6605394722518515 0.6605394722518516 1.252375 -91.556053 1.827583460367510 1.827583460367509 1.409796 -27.006546 1.482258783392487 1.482258783392488 0.148511 -169.229373 0.1485295339221232 0.1485295339221233 1.349466 61.968596 1.753800062701494 1.753800062701494 0.193371 -158.732440 0.1935288964653510 0.1935288964653510 0.408883 105.088396 0.4199100508706138 0.4199100508706138 0.178543 -48.958839 0.1790836490491233 0.1790836490491232 1.292588 -42.585688 1.446048832279763 1.446048832279763 1.087096 11.656033 1.094097652100984 1.094097652100984 1.352795 -8.398114 1.358947908427035 1.358947908427035 1.432530 17.693622 1.464000782315380 1.464000782315380 0.296809 73.880342 0.3009092014525799 0.3009092014525800 0.623588 -69.824923 0.6621341112075102 0.6621341112075103 ELLIPTIC_INC_FK_TEST: ELLIPTIC_INC_FK returns values of the incomplete elliptic integral of the first kind, with parameters PHI, K. PHI K F(PHI,K) F(PHI,K) Tabulated Calculated 0.343091 2.712953 0.4340870330108736 0.4340870330108734 1.302990 0.127952 1.307312511398114 1.307312511398114 0.652363 -1.429438 0.8005154258533936 0.8005154258533933 0.404602 -1.981659 0.4656721451084328 0.4656721451084328 0.068846 3.894802 0.6969849613441773E-01 0.6969849613441774E-01 0.096961 -1.042486 0.9712646708750489E-01 0.9712646708750490E-01 0.630370 0.864114 0.6632598061016007 0.6632598061016008 1.252375 -1.049058 2.230867785857900 2.230867785857911 1.409796 -0.302406 1.439846282888019 1.439846282888019 0.148511 -6.574289 0.2043389243773096 0.2043389243773098 1.349466 0.698740 1.537183574881771 1.537183574881770 0.193371 -5.125586 0.2749229901565622 0.2749229901565621 0.408883 2.074948 0.4828388342828284 0.4828388342828284 0.178543 -1.670886 0.1812848567886627 0.1812848567886627 1.292588 -0.484360 1.360729522341841 1.360729522341841 1.087096 0.139306 1.090396809120270 1.090396809120270 1.352795 -0.094653 1.355363051581808 1.355363051581808 1.432530 0.197721 1.445462819732441 1.445462819732441 0.296809 1.788160 0.3125355489354676 0.3125355489354676 0.623588 -1.077781 0.6775731623807174 0.6775731623807173 ELLIPTIC_INC_FM_TEST: ELLIPTIC_INC_FM returns values of the incomplete elliptic integral of the first kind, with parameters PHI, M. PHI M F(PHI,M) F(PHI,M) Tabulated Calculated 0.343091 8.450690 0.4804314075855023 0.4804314075855022 1.302990 0.603988 1.535634981092025 1.535634981092026 0.652363 0.179413 0.6602285297476601 0.6602285297476599 0.404602 0.709569 0.4125884303785135 0.4125884303785134 0.068846 133.964339 0.7964566007155376E-01 0.7964566007155374E-01 0.096961 47.966214 0.1062834070535258 0.1062834070535258 0.630370 2.172071 0.7733990864393913 0.7733990864393913 1.252375 0.002038 1.252862499892228 1.252862499892228 1.409796 0.360004 1.549988686611532 1.549988686611532 0.148511 0.621954 0.1488506735822822 0.1488506735822822 1.349466 0.883422 1.892229900799662 1.892229900799662 0.193371 0.203429 0.1936153327753556 0.1936153327753556 0.408883 5.772526 0.5481932935424454 0.5481932935424454 0.178543 11.148539 0.1911795073571756 0.1911795073571756 1.292588 0.288924 1.379225069349756 1.379225069349755 1.087096 0.716662 1.261282453331402 1.261282453331402 1.352795 0.476062 1.535239838525378 1.535239838525377 1.432530 0.609495 1.739782418156071 1.739782418156072 0.296809 8.902277 0.3616930047198503 0.3616930047198503 0.623588 0.543444 0.6458627645916422 0.6458627645916422 ELLIPTIC_INC_EA_TEST: ELLIPTIC_INC_EA returns values of the incomplete elliptic integral of the second kind, with parameters PHI, A. PHI A E(PHI,A) E(PHI,A) Tabulated Calculated 0.343091 123.082123 0.3384181367348019 0.3384181367348018 1.302990 11.269317 1.292924624509506 1.292924624509507 0.652363 -94.888065 0.6074183768796306 0.6074183768796306 0.404602 -99.714079 0.3939726730783567 0.3939726730783568 0.068846 57.058810 0.6880814097089803E-01 0.6880814097089803E-01 0.096961 -19.713633 0.9694364733768240E-01 0.9694364733768239E-01 0.630370 56.312303 0.6025937791452033 0.6025937791452034 1.252375 -91.556053 0.9500549494837583 0.9500549494837583 1.409796 -27.006546 1.342783372140486 1.342783372140486 0.148511 -169.229373 0.1484915631401388 0.1484915631401388 1.349466 61.968596 1.085432887050926 1.085432887050926 0.193371 -158.732440 0.1932136916085597 0.1932136916085597 0.408883 105.088396 0.3983689593057807 0.3983689593057807 0.178543 -48.958839 0.1780054133336934 0.1780054133336934 1.292588 -42.585688 1.164525270273536 1.164525270273536 1.087096 11.656033 1.080167047541845 1.080167047541845 1.352795 -8.398114 1.346684963830312 1.346684963830312 1.432530 17.693622 1.402100272685504 1.402100272685504 0.296809 73.880342 0.2928091845544553 0.2928091845544553 0.623588 -69.824923 0.5889342583405707 0.5889342583405708 ELLIPTIC_INC_EK_TEST: ELLIPTIC_INC_EK returns values of the incomplete elliptic integral of the second kind, with parameters PHI, K. PHI K E(PHI,K) E(PHI,K) Tabulated Calculated 0.343091 2.712953 0.2852345328295404 0.2852345328295403 1.302990 0.127952 1.298690225567921 1.298690225567921 0.652363 -1.429438 0.5508100202571943 0.5508100202571941 0.404602 -1.981659 0.3575401358115371 0.3575401358115370 0.068846 3.894802 0.6801307805507453E-01 0.6801307805507455E-01 0.096961 -1.042486 0.9679584980231837E-01 0.9679584980231838E-01 0.630370 0.864114 0.6003112504412838 0.6003112504412839 1.252375 -1.049058 0.8996717721794724 0.8996717721794723 1.409796 -0.302406 1.380715261453875 1.380715261453875 0.148511 -6.574289 0.1191644625202453 0.1191644625202453 1.349466 0.698740 1.196994838171557 1.196994838171556 0.193371 -5.125586 0.1536260979667945 0.1536260979667945 0.408883 2.074948 0.3546768920544152 0.3546768920544152 0.178543 -1.670886 0.1758756066650882 0.1758756066650882 1.292588 -0.484360 1.229819109410569 1.229819109410569 1.087096 0.139306 1.083810661143370 1.083810661143370 1.352795 -0.094653 1.350233781573780 1.350233781573780 1.432530 0.197721 1.419775884709218 1.419775884709217 0.296809 1.788160 0.2824895528020034 0.2824895528020034 0.623588 -1.077781 0.5770427720982867 0.5770427720982867 ELLIPTIC_INC_EM_TEST: ELLIPTIC_INC_EM returns values of the incomplete elliptic integral of the second kind, with parameters PHI, M. PHI M E(PHI,M) E(PHI,M) Tabulated Calculated 0.343091 8.450690 0.2732317284159052 0.2732317284159051 1.302990 0.603988 1.124749725099781 1.124749725099781 0.652363 0.179413 0.6446601913679151 0.6446601913679149 0.404602 0.709569 0.3968902354370061 0.3968902354370061 0.068846 133.964339 0.6063960799944668E-01 0.6063960799944667E-01 0.096961 47.966214 0.8909411577948728E-01 0.8909411577948728E-01 0.630370 2.172071 0.5324020148020150 0.5324020148020150 1.252375 0.002038 1.251888640660265 1.251888640660265 1.409796 0.360004 1.288971161916260 1.288971161916260 0.148511 0.621954 0.1481718153599732 0.1481718153599732 1.349466 0.883422 1.038090185639913 1.038090185639913 0.193371 0.203429 0.1931275771541276 0.1931275771541275 0.408883 5.772526 0.3304419611986801 0.3304419611986802 0.178543 11.148539 0.1673947960639630 0.1673947960639630 1.292588 0.288924 1.214501175324736 1.214501175324735 1.087096 0.716662 0.9516560179840655 0.9516560179840655 1.352795 0.476062 1.203682959526176 1.203682959526176 1.432530 0.609495 1.206426326185419 1.206426326185419 0.296809 8.902277 0.2522791382096692 0.2522791382096691 0.623588 0.543444 0.6026499038720986 0.6026499038720985 ELLIPTIC_INC_PIA_TEST: ELLIPTIC_INC_PIA returns values of the incomplete elliptic integral of the third kind, with parameters PHI, N, A. PHI N A PI(PHI,N,A) PI(PHI,N,A) Tabulated Calculated 0.343091 8.064681 88.878225 0.7099335174334724 0.7099335174334722 0.882309 -0.284059 -86.552087 0.9601963779142505 0.9601963779142507 0.404602 -5.034023 -116.619570 0.3362852532098376 0.3362852532098377 0.995831 -1.244606 -9.742878 0.7785343427543768 0.7785343427543769 0.630370 1.465982 65.734809 0.8578897552144780 0.8578897552144780 0.002888 95338.128573 -115.038772 0.4630772344931844E-02 0.4630772344931842E-02 0.148511 -44.431306 124.942118 0.1173842687902911 0.1173842687902912 1.320800 -0.802937 -89.787044 1.505788070660267 1.505788070660267 0.408883 5.218883 -98.426738 0.7213264194624553 0.7213264194624552 0.552337 2.345822 -53.749362 0.8073261799642218 0.8073261799642221 1.087096 0.157358 68.280476 1.402853811110838 1.402853811110838 0.712818 1.926593 20.821747 1.259245331474513 1.259245331474513 0.296809 6.113983 -29.104236 0.3779079263971614 0.3779079263971614 0.291091 1.805711 -37.801767 0.3088493910496766 0.3088493910496766 0.969503 -0.407285 -55.811734 0.9782829177005183 0.9782829177005182 1.122289 -0.941640 -37.665946 0.9430491574504173 0.9430491574504173 1.295912 0.700966 -80.094082 3.320796277384155 3.320796277384156 1.116491 -1.019831 52.238065 0.9730988737054799 0.9730988737054804 1.170719 -0.451080 74.309452 1.301988094953789 1.301988094953789 1.199361 0.602882 -17.229207 1.645583604452590 1.645583604452591 ELLIPTIC_INC_PIK_TEST: ELLIPTIC_INC_PIK returns values of the incomplete elliptic integral of the third kind, with parameters PHI, N, K. PHI N K Pi(PHI,N,K) Pi(PHI,N,K) Tabulated Calculated 0.343091 8.064681 1.959037 0.7982975462595892 0.7982975462595890 0.882309 -0.284059 -1.123742 1.024022134726036 1.024022134726036 0.404602 -5.034023 -2.317629 0.4015812085264200 0.4015812085264200 0.995831 -1.244606 -0.120258 0.7772649487439858 0.7772649487439859 0.630370 1.465982 1.008703 0.8737159913132074 0.8737159913132075 0.002888 95338.128573 -103.367749 0.4733334297691273E-02 0.4733334297691271E-02 0.148511 -44.431306 4.853800 0.1280656893638068 0.1280656893638067 1.320800 -0.802937 -1.016577 1.594376037512564 1.594376037512565 0.408883 5.218883 -1.943415 0.8521145133671923 0.8521145133671921 0.552337 2.345822 -0.887659 0.8154325229803082 0.8154325229803081 1.087096 0.157358 0.816049 1.315945140754270 1.315945140754270 0.712818 1.926593 0.299455 1.253946231484240 1.253946231484240 0.296809 6.113983 -0.704423 0.3796503567258643 0.3796503567258642 0.291091 1.805711 -0.926652 0.3111034454739552 0.3111034454739551 0.969503 -0.407285 -0.696261 0.9442477901112342 0.9442477901112344 1.122289 -0.941640 -0.445393 0.9153111661980959 0.9153111661980956 1.295912 0.700966 -0.910458 2.842080644328393 2.842080644328393 1.116491 -1.019831 0.618750 0.9263253777034376 0.9263253777034379 1.170719 -0.451080 0.867231 1.212396018757624 1.212396018757624 1.199361 0.602882 -0.199677 1.628083572710471 1.628083572710471 ELLIPTIC_INC_PIM_TEST: ELLIPTIC_INC_PIM returns values of the incomplete elliptic integral of the third kind, with parameters PHI, N, M. PHI N M PI(PHI,N,M) PI(PHI,N,M) Tabulated Calculated 0.343091 8.064681 7.330123 1.046934980078500 1.046934980078499 0.882309 -0.284059 0.110881 0.8421144481406690 0.8421144481406688 0.404602 -5.034023 0.282836 0.3321642201520043 0.3321642201520044 0.995831 -1.244606 0.638300 0.8483033529960849 0.8483033529960846 0.630370 1.465982 2.294719 1.055753817656772 1.055753817656772 0.002888 95338.128573 42062.553298 0.5108896144265593E-02 0.5108896144265589E-02 0.148511 -44.431306 39.239434 0.1426848042785896 0.1426848042785896 1.320800 -0.802937 0.008002 1.031350958206424 1.031350958206424 0.408883 5.218883 0.719058 0.7131013701418496 0.7131013701418496 0.552337 2.345822 0.970377 0.8268044665355507 0.8268044665355507 1.087096 0.157358 1.098881 1.576328678960150 1.576328678960149 0.712818 1.926593 1.398067 1.542817120857211 1.542817120857211 0.296809 6.113983 4.641022 0.4144629799126912 0.4144629799126910 0.291091 1.805711 4.455969 0.3313231611366746 0.3313231611366746 0.969503 -0.407285 0.313145 0.9195822851915201 0.9195822851915201 1.122289 -0.941640 0.368644 0.9422320754002217 0.9422320754002216 1.295912 0.700966 0.066782 2.036599002815859 2.036599002815860 1.116491 -1.019831 0.963554 1.076799231499882 1.076799231499883 1.170719 -0.451080 1.060209 1.416084462957852 1.416084462957854 1.199361 0.602882 0.468716 1.824124922310891 1.824124922310892 jacobi_cn_test: jacobi_cn() evaluates the Jacobi elliptic function CN. U M Exact CN CN(U,M) 0.1000 0.0000 0.9950041652780258 0.9950041652780258 0.2000 0.0000 0.9800665778412416 0.9800665778412416 0.5000 0.0000 0.8775825618903726 0.8775825618903728 1.0000 0.0000 0.5403023058681397 0.5403023058681398 2.0000 0.0000 -0.4161468365471424 -0.4161468365471424 0.1000 0.5000 0.9950124626090582 0.9950124626090583 0.2000 0.5000 0.9801976276784098 0.9801976276784097 0.5000 0.5000 0.8822663948904403 0.8822663948904402 1.0000 0.5000 0.5959765676721407 0.5959765676721407 2.0000 0.5000 -0.1031836155277618 -0.1031836155277620 0.1000 1.0000 0.9950207489532265 0.9950207489532266 0.2000 1.0000 0.9803279976447253 0.9803279976447253 0.5000 1.0000 0.8868188839700739 0.8868188839700740 1.0000 1.0000 0.6480542736638853 0.6480542736638855 2.0000 1.0000 0.2658022288340797 0.2658022288340797 4.0000 1.0000 0.3661899347368653E-01 0.3661899347368653E-01 -0.2000 1.0000 0.9803279976447253 0.9803279976447253 -0.5000 1.0000 0.8868188839700739 0.8868188839700740 -1.0000 1.0000 0.6480542736638853 0.6480542736638855 -2.0000 1.0000 0.2658022288340797 0.2658022288340797 jacobi_dn_test: jacobi_dn() evaluates the Jacobi elliptic function DN. U M Exact DN DN(U,M) 0.1000 0.0000 1.000000000000000 1.000000000000000 0.2000 0.0000 1.000000000000000 1.000000000000000 0.5000 0.0000 1.000000000000000 1.000000000000000 1.0000 0.0000 1.000000000000000 1.000000000000000 2.0000 0.0000 1.000000000000000 1.000000000000000 0.1000 0.5000 0.9975093485144243 0.9975093485144244 0.2000 0.5000 0.9901483195224799 0.9901483195224799 0.5000 0.5000 0.9429724257773857 0.9429724257773857 1.0000 0.5000 0.8231610016315963 0.8231610016315963 2.0000 0.5000 0.7108610477840873 0.7108610477840874 0.1000 1.0000 0.9950207489532265 0.9950207489532266 0.2000 1.0000 0.9803279976447253 0.9803279976447253 0.5000 1.0000 0.8868188839700739 0.8868188839700740 1.0000 1.0000 0.6480542736638853 0.6480542736638855 2.0000 1.0000 0.2658022288340797 0.2658022288340797 4.0000 1.0000 0.3661899347368653E-01 0.3661899347368653E-01 -0.2000 1.0000 0.9803279976447253 0.9803279976447253 -0.5000 1.0000 0.8868188839700739 0.8868188839700740 -1.0000 1.0000 0.6480542736638853 0.6480542736638855 -2.0000 1.0000 0.2658022288340797 0.2658022288340797 jacobi_sn_test: jacobi_sn() evaluates the Jacobi elliptic function SN. U M Exact SN SN(U,M) 0.1000 0.0000 0.9983341664682815E-01 0.9983341664682815E-01 0.2000 0.0000 0.1986693307950612 0.1986693307950612 0.5000 0.0000 0.4794255386042030 0.4794255386042030 1.0000 0.0000 0.8414709848078965 0.8414709848078965 2.0000 0.0000 0.9092974268256817 0.9092974268256817 0.1000 0.5000 0.9975068547462485E-01 0.9975068547462485E-01 0.2000 0.5000 0.1980217429819704 0.1980217429819704 0.5000 0.5000 0.4707504736556573 0.4707504736556573 1.0000 0.5000 0.8030018248956439 0.8030018248956439 2.0000 0.5000 0.9946623253580177 0.9946623253580177 0.1000 1.0000 0.9966799462495582E-01 0.9966799462495582E-01 0.2000 1.0000 0.1973753202249040 0.1973753202249040 0.5000 1.0000 0.4621171572600098 0.4621171572600097 1.0000 1.0000 0.7615941559557649 0.7615941559557649 2.0000 1.0000 0.9640275800758169 0.9640275800758169 4.0000 1.0000 0.9993292997390670 0.9993292997390670 -0.2000 1.0000 -0.1973753202249040 -0.1973753202249040 -0.5000 1.0000 -0.4621171572600098 -0.4621171572600097 -1.0000 1.0000 -0.7615941559557649 -0.7615941559557649 -2.0000 1.0000 -0.9640275800758169 -0.9640275800758169 ELLIPTIC_INTEGRAL_TEST Normal end of execution. 09 September 2021 10:12:36.027 AM