04 March 2022 02:34:42 PM ELLIPTIC_INTEGRAL_TEST C++ 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) 1.51e-78 1.51e-78 8.137884587711593e+38 3.01e-78 5.5e-79 9.524521540989471e+38 0 3.01e-78 9.053919509295885e+38 9.9e+74 5.5e-79 5.629713505821428e-36 0 9.9e+74 4.992318443077758e-38 9.9e+74 9.9e+74 3.178208630818641e-38 RC - Error! Invalid input arguments. X = 0 Y = 2e-78 0 2e-78 ***Error*** 0 0.25 3.141592653589793 0.0625 0.125 3.141592653589793 2.25 2 0.6931471805599454 0.01 1 1.478037662374775 0.02 1 1.443406235712271 0.05 1 1.380231154269966 0.1 1 1.316609847527586 0.2 1 1.237829897094659 0.4 1 1.143920647968054 0.6 1 1.082636119571208 0.8 1 1.036747571331046 1 1 1 1.2 1 0.9693519329631458 1.5 1 0.9312298594527122 2 1 0.8813735870195432 3 1 0.8104969894767539 4 1 0.7603459963009465 5 1 0.7218177375894052 10 1 0.6061488197440222 20 1 0.4997299176960261 50 1 0.3777315372940898 100 1 0.3008302149854818 1000 1 0.131198146266784 10000 1 0.05298557300099017 100000 1 0.02039555141711115 1000000 1 0.007600906009995943 10000000 1 0.002767687204982141 100000000 1 0.0009903487599553565 1000000000 1 0.0003495828416193509 10000000000 1 0.0001220607264611548 1000000000000 1 1.450865773853122e-05 1000000000000000 1 5.680252434588194e-07 1e+20 1 2.37189981105004e-09 1e+30 1 3.523192357547063e-14 1e+40 1 4.674484904044085e-19 1e+50 1 5.825777450541109e-24 RC_TEST2 Compare LOG(X)/(X-1) and ARCTAN(X) with values based on RC. X From LOG From RC 0.2 2.011797390542625 2.011797390542625 0.4 1.527151219790258 1.527151219790258 0.6 1.277064059414976 1.277064059414977 0.8 1.115717756571049 1.115717756571049 1 **** ZERO DIVIDE ***** 1 1 0.9116077839697732 0.911607783969773 1 0.8411805915530323 0.8411805915530324 2 0.7833393820762259 0.7833393820762258 2 0.7347333311276488 0.7347333311276486 2 0.6931471805599453 0.6931471805599454 Extreme values of X X From LOG From RC 1e-75 172.6938819745534 172.6938819745534 1e-65 149.668031044613 149.668031044613 1e-55 126.6421801146725 126.6421801146725 1e-45 103.6163291847321 103.616329184732 1e-35 80.59047825479161 80.59047825479161 1e-25 57.56462732485114 57.56462732485113 1e-15 34.53877639491072 34.53877639491072 1e-05 11.51304059537618 11.51304059537618 1e+05 0.0001151304059537618 0.0001151304059537618 1e+15 3.453877639491072e-14 3.453877639491072e-14 1e+25 5.756462732485114e-24 5.756462732485114e-24 1e+35 8.059047825479162e-34 8.059047825479158e-34 1e+45 1.036163291847321e-43 1.036163291847321e-43 1e+55 1.266421801146725e-53 1.266421801146725e-53 1e+65 1.49668031044613e-63 1.49668031044613e-63 1e+75 1.726938819745534e-73 1.726938819745534e-73 X From ARCTAN From RC RC - Error! Invalid input arguments. X = 1e+75 Y = 1e+75 1e-75 1e-75 0 1e-15 1e-15 9.999999999999999e-16 0.001 0.0009999996666668668 0.0009999996666668666 0.1 0.09966865249116204 0.09966865249116202 0.2 0.1973955598498808 0.1973955598498808 0.5 0.4636476090008061 0.4636476090008061 1 0.7853981633974483 0.7853981633974482 2 1.10714871779409 1.107148717794091 5 1.373400766945016 1.373400766945016 1e+01 1.471127674303735 1.471127674303734 1e+03 1.56979632712823 1.56979632712823 1e+15 1.570796326794896 1.570796326794896 1e+75 1.570796326794897 1.570796326794897 RD_TEST RD evaluates the Carlson elliptic integral of the second kind, RD(X,Y,Z) X Y Z RD(X,Y,Z) 0 6.010000000000001e-51 6.010000000000001e-51 5.057075390167092e+75 5.5e-79 6.010000000000001e-51 6.010000000000001e-51 5.057075390167032e+75 0 6.010000000000001e-51 9.9e+47 3.455579458524223e-70 5.5e-79 6.010000000000001e-51 9.9e+47 3.455579458524223e-70 0 9.9e+47 6.010000000000001e-51 5.016827696801392e+26 5.5e-79 9.9e+47 6.010000000000001e-51 5.016827696801343e+26 0 9.9e+47 9.9e+47 2.391984406816877e-72 5.5e-79 9.9e+47 9.9e+47 2.391984406816877e-72 3.01e-51 3.01e-51 6.010000000000001e-51 3.170935022408316e+75 3.01e-51 3.01e-51 9.9e+47 3.444999003763636e-70 9.9e+47 9.9e+47 6.010000000000001e-51 3.908848372573853e-23 9.9e+47 9.9e+47 9.9e+47 1.015189712383042e-72 RD - Error! Invalid input arguments. X = 0 Y = 3.01e-51 Z = 1 0 3.01e-51 1 ***Error*** 0 2 1 1.797210352103389 0.5 1 1e-10 424255.9649759194 0.5 1 1e-05 1333.576985789446 0.5 1 0.01 35.43137955816859 0.5 1 0.1 8.049184457709792 0.5 1 0.2 4.795496764410121 0.5 1 0.5 2.260648559158617 0.5 1 1 1.210841860059132 0.5 1 2 0.617673967507255 0.5 1 5 0.2361769958541499 0.5 1 10 0.108671998114634 0.5 1 100 0.006540379849123936 0.5 1 100000 5.320236560151541e-07 0.5 1 10000000000 3.409325949193374e-14 RF_TEST RF evaluates the Carlson elliptic integral of the first kind, RF(X,Y,Z) X Y Z RF(X,Y,Z) 1.51e-78 1.51e-78 1.51e-78 8.137884587711593e+38 1.51e-78 1.51e-78 9.9e+74 5.613664399997798e-36 0 3.01e-78 3.01e-78 9.053919509295885e+38 0 3.01e-78 9.9e+74 5.624731938415326e-36 0 9.9e+74 9.9e+74 4.992318443077759e-38 9.9e+74 9.9e+74 9.9e+74 3.178208630818641e-38 5.5e-79 3.01e-78 3.01e-78 7.198956468812792e+38 5.5e-79 3.01e-78 9.9e+74 5.613420743331975e-36 5.5e-79 9.9e+74 9.9e+74 4.992318443077759e-38 RF - Error! Invalid input arguments. X = 0 Y = 2e-78 Z = 1 0 2e-78 1 ***Error*** 0 1 2 1.31102877714606 0.5 1 1 1.110720734539592 0.5 1 1.1 1.091430716268119 0.5 1 1.2 1.073732561377385 0.5 1 1.3 1.057389655801202 0.5 1 1.4 1.042214695930046 0.5 1 1.5 1.028056801052127 0.5 1 1.6 1.014792597551546 0.5 1 1.7 1.002319885847406 0.5 1 1.8 0.9905530382414446 0.5 1 1.9 0.9794195874708435 0.5 1 2 0.9688576532724523 0.5 1 2.2 0.9492423586314841 0.5 1 2.4 0.931359056602438 0.5 1 2.6 0.9149398964447096 0.5 1 2.8 0.8997743463505848 0.5 1 3 0.8856939232035483 0.5 1 3.5 0.8543997654075564 0.5 1 4 0.8275182379903345 0.5 1 4.5 0.8040168167992912 0.5 1 5 0.7831840398091505 0.5 1 6 0.7476135036481746 0.5 1 7 0.7180694683312081 0.5 1 8 0.6929108826625124 0.5 1 9 0.6710782484938838 0.5 1 10 0.6518490214136576 0.5 1 20 0.5331872892861481 0.5 1 30 0.4706527717638377 0.5 1 40 0.4295233682160168 0.5 1 50 0.3994861473220863 0.5 1 100 0.3163981445460594 0.5 1 200 0.2479287246742144 0.5 1 500 0.1771580322263678 0.5 1 1000 0.1361926299714245 0.5 1 10000 0.05456849363690315 0.5 1 100000 0.02089626719954944 0.5 1 1000000 0.007759252354859355 0.5 1 100000000 0.001006183477210615 0.5 1 10000000000 0.0001236441982979439 0.5 1 1000000000000 1.46670049223499e-05 0.5 1 1000000000000000 5.73032621078277e-07 0.5 1 1e+20 2.387734529432078e-09 0.5 1 1e+30 3.539027075929101e-14 0.5 1 1e+40 4.690319622426123e-19 0.5 1 1e+50 5.841612168923146e-24 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) 1.01e-26 1.01e-26 1.01e-26 2.01e-26 6.363797977910284e+38 1.01e-26 1.01e-26 2.99e+24 2.01e-26 59698096408103.98 0 2.01e-26 2.01e-26 2.01e-26 8.268315690384853e+38 0 2.01e-26 2.99e+24 2.01e-26 86315661487498.53 0 2.99e+24 2.99e+24 2.01e-26 1.11165983529589e-11 2.99e+24 2.99e+24 2.99e+24 2.01e-26 3.333899154957826e-35 5.5e-79 2.01e-26 2.01e-26 2.01e-26 8.268315690384853e+38 5.5e-79 2.01e-26 2.99e+24 2.01e-26 86315661487498.53 5.5e-79 2.99e+24 2.99e+24 2.01e-26 1.11165983529589e-11 2.01e-26 2.01e-26 2.01e-26 2.01e-26 3.509182168450738e+38 1.01e-26 1.01e-26 1.01e-26 2.99e+24 9.983650737892871e-12 1.01e-26 1.01e-26 2.99e+24 2.99e+24 3.353865073488965e-35 0 2.01e-26 2.01e-26 2.99e+24 1.11165983529589e-11 0 2.01e-26 2.99e+24 2.99e+24 3.374118957422856e-35 0 2.99e+24 2.99e+24 2.99e+24 4.557265740116441e-37 2.99e+24 2.99e+24 2.99e+24 2.99e+24 1.934163652061004e-37 5.5e-79 2.01e-26 2.01e-26 2.99e+24 1.11165983529589e-11 5.5e-79 2.01e-26 2.99e+24 2.99e+24 3.374118957422856e-35 5.5e-79 2.99e+24 2.99e+24 2.99e+24 4.557265740116441e-37 2.01e-26 2.01e-26 2.01e-26 2.99e+24 7.077046312962523e-12 RJ - Error! Invalid input arguments. X = 0 Y = 1.9e-26 Z = 1.9e-26 P = 1 0 1.9e-26 1.9e-26 1 ***Error*** 2 3 4 5 0.1429757966715675 0.5 1 1 0.25 2.608105757997978 0.5 1 1 0.75 1.442864193614197 0.5 1 1 1 1.210841860059132 0.5 1 1 2 0.7670625432950464 0.5 1 2 0.25 2.008380291058661 0.5 1 2 0.75 1.136845217951276 0.5 1 2 1.5 0.7460643441600711 0.5 1 2 4 0.3794195060366037 0.5 1 5 0.25 1.370892718222587 0.5 1 5 0.75 0.7949204422899481 0.5 1 5 3 0.338529421141784 0.5 1 5 10 0.139847651098525 0.5 1 10 0.25 1.005572682199914 0.5 1 10 0.75 0.5908850286211613 0.5 1 10 5 0.1811791604390096 0.5 1 10 20 0.06283564851298871 0.5 1 100 0.25 0.3343272158567165 0.5 1 100 0.75 0.2006464395741285 0.5 1 100 50 0.01167793209710091 0.5 1 100 200 0.003581148146400939 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 1.570796326794897 1.570796326794897 5 1.573792130924768 1.573792130924768 10 1.582842804338351 1.582842804338351 15 1.59814200211254 1.59814200211254 20 1.620025899124204 1.620025899124204 25 1.64899521847853 1.648995218478531 30 1.685750354812596 1.685750354812596 35 1.731245175657058 1.731245175657058 40 1.786769134885021 1.786769134885021 45 1.854074677301372 1.854074677301372 50 1.935581096004722 1.935581096004722 55 2.034715312185791 2.03471531218579 60 2.156515647499643 2.156515647499643 65 2.308786798167196 2.308786798167196 70 2.504550079001634 2.504550079001633 75 2.768063145368768 2.768063145368768 80 3.153385251887839 3.153385251887837 85 3.831741999784146 3.831741999784147 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 1.570796326794897 1.570796326794897 0.223607 1.591003453790792 1.591003453790792 0.316228 1.612441348720219 1.612441348720219 0.387298 1.63525673226458 1.63525673226458 0.447214 1.659623598610528 1.659623598610528 0.5 1.685750354812596 1.685750354812596 0.547723 1.713889448178791 1.713889448178791 0.591608 1.744350597225613 1.744350597225613 0.632456 1.777519371491253 1.777519371491253 0.67082 1.813883936816983 1.813883936816982 0.707107 1.854074677301372 1.854074677301372 0.74162 1.898924910271554 1.898924910271553 0.774597 1.949567749806026 1.949567749806026 0.806226 2.007598398424376 2.007598398424376 0.83666 2.075363135292469 2.07536313529247 0.866025 2.156515647499643 2.156515647499643 0.894427 2.257205326820854 2.257205326820854 0.921954 2.38901648632558 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 1.570796326794897 1.570796326794897 0.05 1.591003453790792 1.591003453790793 0.1 1.612441348720219 1.61244134872022 0.15 1.63525673226458 1.63525673226458 0.2 1.659623598610528 1.659623598610528 0.25 1.685750354812596 1.685750354812596 0.3 1.713889448178791 1.713889448178791 0.35 1.744350597225613 1.744350597225613 0.4 1.777519371491253 1.777519371491253 0.45 1.813883936816983 1.813883936816982 0.5 1.854074677301372 1.854074677301372 0.55 1.898924910271554 1.898924910271553 0.6 1.949567749806026 1.949567749806026 0.65 2.007598398424376 2.007598398424376 0.7 2.075363135292469 2.075363135292469 0.75 2.156515647499643 2.156515647499643 0.8 2.257205326820854 2.257205326820854 0.85 2.38901648632558 2.38901648632558 0.9 2.578092113348173 2.578092113348173 0.95 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 1.570796326794897 1.570796326794897 5 1.567809073977622 1.567809073977621 10 1.558887196601596 1.558887196601596 15 1.544150496914673 1.544150496914673 20 1.523799205259774 1.523799205259774 25 1.498114928422116 1.498114928422115 30 1.467462209339427 1.467462209339427 35 1.432290969306756 1.432290969306756 40 1.393140248523812 1.393140248523812 45 1.350643881047676 1.350643881047676 50 1.305539094297794 1.305539094297794 55 1.258679624779997 1.258679624779997 60 1.211056027568459 1.21105602756846 65 1.163827964493139 1.163827964493139 70 1.118377737969864 1.118377737969863 75 1.076405113076403 1.076405113076403 80 1.04011439570601 1.04011439570601 85 1.012663506234396 1.012663506234396 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 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 0.5 1.467462209339427 1.467462209339427 0.547723 1.445363064412665 1.445363064412665 0.591608 1.422691133490879 1.422691133490879 0.632456 1.399392138897432 1.399392138897432 0.67082 1.375401971871116 1.375401971871116 0.707107 1.350643881047676 1.350643881047676 0.74162 1.32502449795823 1.32502449795823 0.774597 1.298428035046913 1.298428035046913 0.806226 1.270707479650149 1.27070747965015 0.83666 1.241670567945823 1.241670567945823 0.866025 1.211056027568459 1.21105602756846 0.894427 1.178489924327839 1.178489924327839 0.921954 1.143395791883166 1.143395791883166 0.948683 1.104774732704073 1.104774732704073 0.974679 1.060473727766278 1.060473727766278 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 1.570796326794897 1.570796326794897 0.05 1.550973351780472 1.550973351780473 0.1 1.530757636897763 1.530757636897763 0.15 1.510121832092819 1.510121832092819 0.2 1.489035058095853 1.489035058095852 0.25 1.467462209339427 1.467462209339427 0.3 1.445363064412665 1.445363064412665 0.35 1.422691133490879 1.422691133490879 0.4 1.399392138897432 1.399392138897432 0.45 1.375401971871116 1.375401971871116 0.5 1.350643881047676 1.350643881047676 0.55 1.32502449795823 1.32502449795823 0.6 1.298428035046913 1.298428035046913 0.65 1.270707479650149 1.270707479650149 0.7 1.241670567945823 1.241670567945823 0.75 1.211056027568459 1.21105602756846 0.8 1.178489924327839 1.178489924327839 0.85 1.143395791883166 1.143395791883166 0.9 1.104774732704073 1.104774732704073 0.95 1.060473727766278 1.060473727766278 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 30 0.4892245275965397 0.4892245275965397 -10 45 0.5106765677902629 0.5106765677902629 -10 60 0.5460409271920561 0.5460409271920565 -10 77.079 0.6237325893535237 0.6237325893535237 -3 30 0.823045542660675 0.8230455426606752 -3 45 0.8760028274011437 0.8760028274011439 -3 60 0.9660073560143946 0.9660073560143951 -3 77.079 1.171952391481798 1.171952391481798 -1 30 1.177446843000566 1.177446843000566 -1 45 1.273127366749682 1.273127366749682 -1 60 1.440034318657551 1.440034318657551 -1 77.079 1.836472172302591 1.83647217230259 0 30 1.685750354812596 1.685750354812596 0 45 1.854074677301372 1.854074677301372 0 60 2.156515647499643 2.156515647499643 0 77.079 2.908337248444552 2.908337248444551 0.5 30 2.413671504201195 2.413671504201195 0.5 45 2.701287762095351 2.701287762095351 0.5 60 3.234773471249465 3.234773471249465 0.5 77.079 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 0.5 0.4892245275965397 0.4892245275965397 -10 0.707107 0.5106765677902629 0.5106765677902632 -10 0.866025 0.5460409271920561 0.5460409271920565 -10 0.974679 0.6237325893535237 0.6237325893535237 -3 0.5 0.823045542660675 0.8230455426606752 -3 0.707107 0.8760028274011437 0.8760028274011439 -3 0.866025 0.9660073560143946 0.9660073560143951 -3 0.974679 1.171952391481798 1.171952391481798 -1 0.5 1.177446843000566 1.177446843000566 -1 0.707107 1.273127366749682 1.273127366749683 -1 0.866025 1.440034318657551 1.440034318657551 -1 0.974679 1.836472172302591 1.83647217230259 0 0.5 1.685750354812596 1.685750354812596 0 0.707107 1.854074677301372 1.854074677301372 0 0.866025 2.156515647499643 2.156515647499643 0 0.974679 2.908337248444552 2.908337248444551 0.5 0.5 2.413671504201195 2.413671504201195 0.5 0.707107 2.701287762095351 2.701287762095351 0.5 0.866025 3.234773471249465 3.234773471249465 0.5 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 0.25 0.4892245275965397 0.4892245275965397 -10 0.5 0.5106765677902629 0.5106765677902629 -10 0.75 0.5460409271920561 0.5460409271920565 -10 0.95 0.6237325893535237 0.6237325893535228 -3 0.25 0.823045542660675 0.8230455426606752 -3 0.5 0.8760028274011437 0.8760028274011439 -3 0.75 0.9660073560143946 0.9660073560143951 -3 0.95 1.171952391481798 1.171952391481798 -1 0.25 1.177446843000566 1.177446843000566 -1 0.5 1.273127366749682 1.273127366749682 -1 0.75 1.440034318657551 1.440034318657551 -1 0.95 1.836472172302591 1.83647217230259 0 0.25 1.685750354812596 1.685750354812596 0 0.5 1.854074677301372 1.854074677301372 0 0.75 2.156515647499643 2.156515647499643 0 0.95 2.908337248444552 2.908337248444551 0.5 0.25 2.413671504201195 2.413671504201195 0.5 0.5 2.701287762095351 2.701287762095351 0.5 0.75 3.234773471249465 3.234773471249465 0.5 0.95 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 123.082 0.3478806460316299 0.3478806460316299 1.30299 11.2693 1.313180577009584 1.313180577009584 0.652363 -94.8881 0.7037956689264326 0.7037956689264325 0.404602 -99.7141 0.4157626844675118 0.4157626844675119 0.0688464 57.0588 0.06888475483285136 0.06888475483285136 0.0969609 -19.7136 0.09697816754845832 0.0969781675484583 0.63037 56.3123 0.6605394722518515 0.6605394722518516 1.25238 -91.5561 1.82758346036751 1.827583460367509 1.4098 -27.0065 1.482258783392487 1.482258783392488 0.148511 -169.229 0.1485295339221232 0.1485295339221233 1.34947 61.9686 1.753800062701494 1.753800062701494 0.193371 -158.732 0.193528896465351 0.193528896465351 0.408883 105.088 0.4199100508706138 0.4199100508706138 0.178543 -48.9588 0.1790836490491233 0.1790836490491232 1.29259 -42.5857 1.446048832279763 1.446048832279763 1.0871 11.656 1.094097652100984 1.094097652100984 1.35279 -8.39811 1.358947908427035 1.358947908427035 1.43253 17.6936 1.46400078231538 1.46400078231538 0.296809 73.8803 0.3009092014525799 0.30090920145258 0.623588 -69.8249 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 2.71295 0.4340870330108736 0.4340870330108734 1.30299 0.127952 1.307312511398114 1.307312511398114 0.652363 -1.42944 0.8005154258533936 0.8005154258533933 0.404602 -1.98166 0.4656721451084328 0.4656721451084328 0.0688464 3.8948 0.06969849613441773 0.06969849613441774 0.0969609 -1.04249 0.09712646708750489 0.0971264670875049 0.63037 0.864114 0.6632598061016007 0.6632598061016008 1.25238 -1.04906 2.2308677858579 2.230867785857911 1.4098 -0.302406 1.439846282888019 1.439846282888019 0.148511 -6.57429 0.2043389243773096 0.2043389243773098 1.34947 0.69874 1.537183574881771 1.53718357488177 0.193371 -5.12559 0.2749229901565622 0.2749229901565621 0.408883 2.07495 0.4828388342828284 0.4828388342828284 0.178543 -1.67089 0.1812848567886627 0.1812848567886627 1.29259 -0.48436 1.360729522341841 1.360729522341841 1.0871 0.139306 1.09039680912027 1.09039680912027 1.35279 -0.0946527 1.355363051581808 1.355363051581808 1.43253 0.197721 1.445462819732441 1.445462819732441 0.296809 1.78816 0.3125355489354676 0.3125355489354676 0.623588 -1.07778 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 8.45069 0.4804314075855023 0.4804314075855021 1.30299 0.603988 1.535634981092025 1.535634981092026 0.652363 0.179413 0.6602285297476601 0.6602285297476599 0.404602 0.709569 0.4125884303785135 0.4125884303785134 0.0688464 133.964 0.07964566007155376 0.07964566007155374 0.0969609 47.9662 0.1062834070535258 0.1062834070535258 0.63037 2.17207 0.7733990864393913 0.7733990864393913 1.25238 0.00203813 1.252862499892228 1.252862499892228 1.4098 0.360004 1.549988686611532 1.549988686611532 0.148511 0.621954 0.1488506735822822 0.1488506735822822 1.34947 0.883422 1.892229900799662 1.892229900799662 0.193371 0.203429 0.1936153327753556 0.1936153327753556 0.408883 5.77253 0.5481932935424454 0.5481932935424454 0.178543 11.1485 0.1911795073571756 0.1911795073571756 1.29259 0.288924 1.379225069349756 1.379225069349755 1.0871 0.716662 1.261282453331402 1.261282453331402 1.35279 0.476062 1.535239838525378 1.535239838525377 1.43253 0.609495 1.739782418156071 1.739782418156072 0.296809 8.90228 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 123.082 0.3384181367348019 0.3384181367348018 1.30299 11.2693 1.292924624509506 1.292924624509507 0.652363 -94.8881 0.6074183768796306 0.6074183768796306 0.404602 -99.7141 0.3939726730783567 0.3939726730783568 0.0688464 57.0588 0.06880814097089803 0.06880814097089803 0.0969609 -19.7136 0.0969436473376824 0.09694364733768239 0.63037 56.3123 0.6025937791452033 0.6025937791452034 1.25238 -91.5561 0.9500549494837583 0.9500549494837583 1.4098 -27.0065 1.342783372140486 1.342783372140486 0.148511 -169.229 0.1484915631401388 0.1484915631401388 1.34947 61.9686 1.085432887050926 1.085432887050927 0.193371 -158.732 0.1932136916085597 0.1932136916085597 0.408883 105.088 0.3983689593057807 0.3983689593057807 0.178543 -48.9588 0.1780054133336934 0.1780054133336934 1.29259 -42.5857 1.164525270273536 1.164525270273536 1.0871 11.656 1.080167047541845 1.080167047541845 1.35279 -8.39811 1.346684963830312 1.346684963830312 1.43253 17.6936 1.402100272685504 1.402100272685504 0.296809 73.8803 0.2928091845544553 0.2928091845544553 0.623588 -69.8249 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 2.71295 0.2852345328295404 0.2852345328295403 1.30299 0.127952 1.298690225567921 1.298690225567921 0.652363 -1.42944 0.5508100202571943 0.5508100202571941 0.404602 -1.98166 0.3575401358115371 0.357540135811537 0.0688464 3.8948 0.06801307805507453 0.06801307805507455 0.0969609 -1.04249 0.09679584980231837 0.09679584980231838 0.63037 0.864114 0.6003112504412838 0.6003112504412839 1.25238 -1.04906 0.8996717721794724 0.8996717721794723 1.4098 -0.302406 1.380715261453875 1.380715261453875 0.148511 -6.57429 0.1191644625202453 0.1191644625202453 1.34947 0.69874 1.196994838171557 1.196994838171556 0.193371 -5.12559 0.1536260979667945 0.1536260979667945 0.408883 2.07495 0.3546768920544152 0.3546768920544152 0.178543 -1.67089 0.1758756066650882 0.1758756066650882 1.29259 -0.48436 1.229819109410569 1.229819109410569 1.0871 0.139306 1.08381066114337 1.08381066114337 1.35279 -0.0946527 1.35023378157378 1.35023378157378 1.43253 0.197721 1.419775884709218 1.419775884709217 0.296809 1.78816 0.2824895528020034 0.2824895528020034 0.623588 -1.07778 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 8.45069 0.2732317284159052 0.2732317284159052 1.30299 0.603988 1.124749725099781 1.124749725099781 0.652363 0.179413 0.6446601913679151 0.6446601913679149 0.404602 0.709569 0.3968902354370061 0.3968902354370061 0.0688464 133.964 0.06063960799944668 0.06063960799944668 0.0969609 47.9662 0.08909411577948728 0.08909411577948728 0.63037 2.17207 0.532402014802015 0.532402014802015 1.25238 0.00203813 1.251888640660265 1.251888640660265 1.4098 0.360004 1.28897116191626 1.28897116191626 0.148511 0.621954 0.1481718153599732 0.1481718153599732 1.34947 0.883422 1.038090185639913 1.038090185639913 0.193371 0.203429 0.1931275771541276 0.1931275771541275 0.408883 5.77253 0.3304419611986801 0.3304419611986802 0.178543 11.1485 0.167394796063963 0.167394796063963 1.29259 0.288924 1.214501175324736 1.214501175324735 1.0871 0.716662 0.9516560179840655 0.9516560179840655 1.35279 0.476062 1.203682959526176 1.203682959526176 1.43253 0.609495 1.206426326185419 1.206426326185419 0.296809 8.90228 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 8.06468 88.8782 0.7099335174334724 0.7099335174334722 0.882309 -0.284059 -86.5521 0.9601963779142505 0.9601963779142507 0.404602 -5.03402 -116.62 0.3362852532098376 0.3362852532098376 0.995831 -1.24461 -9.74288 0.7785343427543768 0.7785343427543769 0.63037 1.46598 65.7348 0.857889755214478 0.857889755214478 0.00288771 95338.1 -115.039 0.004630772344931844 0.004630772344931842 0.148511 -44.4313 124.942 0.1173842687902911 0.1173842687902912 1.3208 -0.802937 -89.787 1.505788070660267 1.505788070660267 0.408883 5.21888 -98.4267 0.7213264194624553 0.7213264194624552 0.552337 2.34582 -53.7494 0.8073261799642218 0.8073261799642221 1.0871 0.157358 68.2805 1.402853811110838 1.402853811110838 0.712818 1.92659 20.8217 1.259245331474513 1.259245331474513 0.296809 6.11398 -29.1042 0.3779079263971614 0.3779079263971614 0.291091 1.80571 -37.8018 0.3088493910496766 0.3088493910496766 0.969503 -0.407285 -55.8117 0.9782829177005183 0.9782829177005182 1.12229 -0.94164 -37.6659 0.9430491574504173 0.9430491574504173 1.29591 0.700966 -80.0941 3.320796277384155 3.320796277384156 1.11649 -1.01983 52.2381 0.9730988737054799 0.9730988737054804 1.17072 -0.45108 74.3095 1.301988094953789 1.301988094953789 1.19936 0.602882 -17.2292 1.64558360445259 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 8.06468 1.95904 0.7982975462595892 0.798297546259589 0.882309 -0.284059 -1.12374 1.024022134726036 1.024022134726036 0.404602 -5.03402 -2.31763 0.40158120852642 0.40158120852642 0.995831 -1.24461 -0.120258 0.7772649487439858 0.7772649487439859 0.63037 1.46598 1.0087 0.8737159913132074 0.8737159913132075 0.00288771 95338.1 -103.368 0.004733334297691273 0.004733334297691271 0.148511 -44.4313 4.8538 0.1280656893638068 0.1280656893638067 1.3208 -0.802937 -1.01658 1.594376037512564 1.594376037512565 0.408883 5.21888 -1.94341 0.8521145133671923 0.8521145133671921 0.552337 2.34582 -0.887659 0.8154325229803082 0.8154325229803081 1.0871 0.157358 0.816049 1.31594514075427 1.31594514075427 0.712818 1.92659 0.299455 1.25394623148424 1.25394623148424 0.296809 6.11398 -0.704423 0.3796503567258643 0.3796503567258642 0.291091 1.80571 -0.926652 0.3111034454739552 0.3111034454739551 0.969503 -0.407285 -0.696261 0.9442477901112342 0.9442477901112345 1.12229 -0.94164 -0.445393 0.9153111661980959 0.9153111661980956 1.29591 0.700966 -0.910458 2.842080644328393 2.842080644328393 1.11649 -1.01983 0.61875 0.9263253777034376 0.9263253777034379 1.17072 -0.45108 0.867231 1.212396018757624 1.212396018757624 1.19936 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 8.06468 7.33012 1.0469349800785 1.046934980078499 0.882309 -0.284059 0.110881 0.842114448140669 0.8421144481406688 0.404602 -5.03402 0.282836 0.3321642201520043 0.3321642201520044 0.995831 -1.24461 0.6383 0.8483033529960849 0.8483033529960846 0.63037 1.46598 2.29472 1.055753817656772 1.055753817656772 0.00288771 95338.1 42062.6 0.005108896144265593 0.005108896144265589 0.148511 -44.4313 39.2394 0.1426848042785896 0.1426848042785896 1.3208 -0.802937 0.00800215 1.031350958206424 1.031350958206424 0.408883 5.21888 0.719058 0.7131013701418496 0.7131013701418496 0.552337 2.34582 0.970377 0.8268044665355507 0.8268044665355507 1.0871 0.157358 1.09888 1.57632867896015 1.576328678960149 0.712818 1.92659 1.39807 1.542817120857211 1.542817120857211 0.296809 6.11398 4.64102 0.4144629799126912 0.4144629799126911 0.291091 1.80571 4.45597 0.3313231611366746 0.3313231611366746 0.969503 -0.407285 0.313145 0.9195822851915201 0.9195822851915201 1.12229 -0.94164 0.368644 0.9422320754002217 0.9422320754002216 1.29591 0.700966 0.0667821 2.036599002815859 2.03659900281586 1.11649 -1.01983 0.963554 1.076799231499882 1.076799231499883 1.17072 -0.45108 1.06021 1.416084462957852 1.416084462957854 1.19936 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) 0.1 0 0.9950041652780258 0.9950041652780258 0.2 0 0.9800665778412416 0.9800665778412416 0.5 0 0.8775825618903726 0.8775825618903728 1 0 0.5403023058681397 0.5403023058681398 2 0 -0.4161468365471424 -0.4161468365471424 0.1 0.5 0.9950124626090582 0.9950124626090583 0.2 0.5 0.9801976276784098 0.9801976276784097 0.5 0.5 0.8822663948904403 0.8822663948904402 1 0.5 0.5959765676721407 0.5959765676721407 2 0.5 -0.1031836155277618 -0.103183615527762 0.1 1 0.9950207489532265 0.9950207489532266 0.2 1 0.9803279976447253 0.9803279976447253 0.5 1 0.8868188839700739 0.886818883970074 1 1 0.6480542736638853 0.6480542736638855 2 1 0.2658022288340797 0.2658022288340797 4 1 0.03661899347368653 0.03661899347368653 -0.2 1 0.9803279976447253 0.9803279976447253 -0.5 1 0.8868188839700739 0.886818883970074 -1 1 0.6480542736638853 0.6480542736638855 -2 1 0.2658022288340797 0.2658022288340797 jacobi_dn_test: jacobi_dn() evaluates the Jacobi elliptic function DN. U M Exact DN DN(U,M) 0.1 0 1 1 0.2 0 1 1 0.5 0 1 1 1 0 1 1 2 0 1 1 0.1 0.5 0.9975093485144243 0.9975093485144244 0.2 0.5 0.9901483195224799 0.9901483195224799 0.5 0.5 0.9429724257773857 0.9429724257773857 1 0.5 0.8231610016315963 0.8231610016315963 2 0.5 0.7108610477840873 0.7108610477840874 0.1 1 0.9950207489532265 0.9950207489532266 0.2 1 0.9803279976447253 0.9803279976447253 0.5 1 0.8868188839700739 0.886818883970074 1 1 0.6480542736638853 0.6480542736638855 2 1 0.2658022288340797 0.2658022288340797 4 1 0.03661899347368653 0.03661899347368653 -0.2 1 0.9803279976447253 0.9803279976447253 -0.5 1 0.8868188839700739 0.886818883970074 -1 1 0.6480542736638853 0.6480542736638855 -2 1 0.2658022288340797 0.2658022288340797 jacobi_sn_test: jacobi_sn() evaluates the Jacobi elliptic function SN. U M Exact SN SN(U,M) 0.1 0 0.09983341664682815 0.09983341664682815 0.2 0 0.1986693307950612 0.1986693307950612 0.5 0 0.479425538604203 0.479425538604203 1 0 0.8414709848078965 0.8414709848078965 2 0 0.9092974268256817 0.9092974268256817 0.1 0.5 0.09975068547462485 0.09975068547462485 0.2 0.5 0.1980217429819704 0.1980217429819704 0.5 0.5 0.4707504736556573 0.4707504736556573 1 0.5 0.8030018248956439 0.8030018248956439 2 0.5 0.9946623253580177 0.9946623253580177 0.1 1 0.09966799462495582 0.09966799462495582 0.2 1 0.197375320224904 0.197375320224904 0.5 1 0.4621171572600098 0.4621171572600097 1 1 0.7615941559557649 0.7615941559557649 2 1 0.9640275800758169 0.9640275800758169 4 1 0.999329299739067 0.999329299739067 -0.2 1 -0.197375320224904 -0.197375320224904 -0.5 1 -0.4621171572600098 -0.4621171572600097 -1 1 -0.7615941559557649 -0.7615941559557649 -2 1 -0.9640275800758169 -0.9640275800758169 ELLIPTIC_INTEGRAL_TEST Normal end of execution. 04 March 2022 02:34:42 PM