15 September 2021 8:27:07.384 AM LEGENDRE_POLYNOMIAL_TEST: FORTRAN90 version. Test the LEGENDRE_POLYNOMIAL library. P_EXPONENTIAL_PRODUCT_TEST P_EXPONENTIAL_PRODUCT_TEST computes an exponential product table for P(n,x): Tij = integral ( -1 <= x <= +1 ) exp(b*x) P(i,x) P(j,x) dx Maximum degree P = 5 Exponential argument coefficient B = 0.00000 Exponential product table: Col 1 2 3 4 5 Row 1: 2.00000 0.333067E-15 0.735523E-15 0.180411E-15 -0.791034E-15 2: 0.333067E-15 0.666667 0.208167E-15 -0.124900E-15 -0.818789E-15 3: 0.735523E-15 0.208167E-15 0.400000 -0.645317E-15 -0.971445E-16 4: 0.180411E-15 -0.124900E-15 -0.638378E-15 0.285714 -0.222045E-15 5: -0.791034E-15 -0.811851E-15 -0.124900E-15 -0.215106E-15 0.222222 6: -0.165146E-14 -0.513478E-15 -0.291434E-15 -0.381639E-15 -0.693889E-17 Col 6 Row 1: -0.165146E-14 2: -0.506539E-15 3: -0.291434E-15 4: -0.374700E-15 5: -0.693889E-17 6: 0.181818 P_EXPONENTIAL_PRODUCT_TEST P_EXPONENTIAL_PRODUCT_TEST computes an exponential product table for P(n,x): Tij = integral ( -1 <= x <= +1 ) exp(b*x) P(i,x) P(j,x) dx Maximum degree P = 5 Exponential argument coefficient B = 1.00000 Exponential product table: Col 1 2 3 4 5 Row 1: 2.35040 0.735759 0.143126 0.201302E-01 0.221447E-02 2: 0.735759 0.878885 0.306382 0.626050E-01 0.905782E-02 3: 0.143126 0.306382 0.512112 0.194658 0.414752E-01 4: 0.201302E-01 0.626050E-01 0.194658 0.363558 0.143849 5: 0.221447E-02 0.905782E-02 0.414752E-01 0.143849 0.282170 6: 0.199925E-03 0.101492E-02 0.615177E-02 0.313811E-01 0.114325 Col 6 Row 1: 0.199925E-03 2: 0.101492E-02 3: 0.615177E-02 4: 0.313811E-01 5: 0.114325 6: 0.230635 P_INTEGRAL_TEST: P_INTEGRAL returns the integral of P(n,x) over [-1,+1]. N Integral 0 2.00000 1 0.00000 2 0.666667 3 0.00000 4 0.400000 5 0.00000 6 0.285714 7 0.00000 8 0.222222 9 0.00000 10 0.181818 P_POLYNOMIAL_COEFFICIENTS_TEST P_POLYNOMIAL_COEFFICIENTS determines polynomial coefficients of P(n,x). P( 0,x) = 1.00000 P( 1,x) = 1.00000 * x P( 2,x) = 1.50000 * x^ 2 -0.500000 P( 3,x) = 2.50000 * x^ 3 -1.50000 * x P( 4,x) = 4.37500 * x^ 4 -3.75000 * x^ 2 0.375000 P( 5,x) = 7.87500 * x^ 5 -8.75000 * x^ 3 1.87500 * x P( 6,x) = 14.4375 * x^ 6 -19.6875 * x^ 4 6.56250 * x^ 2 -0.312500 P( 7,x) = 26.8125 * x^ 7 -43.3125 * x^ 5 19.6875 * x^ 3 -2.18750 * x P( 8,x) = 50.2734 * x^ 8 -93.8438 * x^ 6 54.1406 * x^ 4 -9.84375 * x^ 2 0.273438 P( 9,x) = 94.9609 * x^ 9 -201.094 * x^ 7 140.766 * x^ 5 -36.0938 * x^ 3 2.46094 * x P(10,x) = 180.426 * x^10 -427.324 * x^ 8 351.914 * x^ 6 -117.305 * x^ 4 13.5352 * x^ 2 -0.246094 P_POLYNOMIAL_PRIME_TEST: P_POLYNOMIAL_PRIME evaluates the derivative of the Legendre polynomial. Computed N X P'(N,X) 0 -1.000000 0.000000000000000 1 -1.000000 1.000000000000000 2 -1.000000 -3.000000000000000 3 -1.000000 6.000000000000000 4 -1.000000 -10.00000000000000 5 -1.000000 15.00000000000000 0 -0.800000 0.000000000000000 1 -0.800000 1.000000000000000 2 -0.800000 -2.400000000000000 3 -0.800000 3.300000000000001 4 -0.800000 -2.960000000000001 5 -0.800000 1.203000000000002 0 -0.600000 0.000000000000000 1 -0.600000 1.000000000000000 2 -0.600000 -1.800000000000000 3 -0.600000 1.199999999999999 4 -0.600000 0.7200000000000008 5 -0.600000 -2.472000000000000 0 -0.400000 0.000000000000000 1 -0.400000 1.000000000000000 2 -0.400000 -1.200000000000000 3 -0.400000 -0.2999999999999998 4 -0.400000 1.880000000000000 5 -0.400000 -1.317000000000000 0 -0.200000 0.000000000000000 1 -0.200000 1.000000000000000 2 -0.200000 -0.6000000000000001 3 -0.200000 -1.200000000000000 4 -0.200000 1.360000000000000 5 -0.200000 0.8879999999999999 0 0.000000 0.000000000000000 1 0.000000 1.000000000000000 2 0.000000 0.000000000000000 3 0.000000 -1.500000000000000 4 0.000000 -0.000000000000000 5 0.000000 1.875000000000000 0 0.200000 0.000000000000000 1 0.200000 1.000000000000000 2 0.200000 0.6000000000000001 3 0.200000 -1.200000000000000 4 0.200000 -1.360000000000000 5 0.200000 0.8879999999999999 0 0.400000 0.000000000000000 1 0.400000 1.000000000000000 2 0.400000 1.200000000000000 3 0.400000 -0.2999999999999998 4 0.400000 -1.880000000000000 5 0.400000 -1.317000000000000 0 0.600000 0.000000000000000 1 0.600000 1.000000000000000 2 0.600000 1.800000000000000 3 0.600000 1.199999999999999 4 0.600000 -0.7200000000000008 5 0.600000 -2.472000000000000 0 0.800000 0.000000000000000 1 0.800000 1.000000000000000 2 0.800000 2.400000000000000 3 0.800000 3.300000000000001 4 0.800000 2.960000000000001 5 0.800000 1.203000000000002 0 1.000000 0.000000000000000 1 1.000000 1.000000000000000 2 1.000000 3.000000000000000 3 1.000000 6.000000000000000 4 1.000000 10.00000000000000 5 1.000000 15.00000000000000 P_POLYNOMIAL_PRIME2_TEST: P_POLYNOMIAL_PRIME2 evaluates the second derivative of the Legendre polynomial. Computed N X P"(N,X) 0 -1.000000 0.000000000000000 1 -1.000000 0.000000000000000 2 -1.000000 3.000000000000000 3 -1.000000 -15.00000000000000 4 -1.000000 45.00000000000000 5 -1.000000 -105.0000000000000 0 -0.800000 0.000000000000000 1 -0.800000 0.000000000000000 2 -0.800000 3.000000000000000 3 -0.800000 -12.00000000000000 4 -0.800000 26.10000000000000 5 -0.800000 -38.64000000000001 0 -0.600000 0.000000000000000 1 -0.600000 0.000000000000000 2 -0.600000 3.000000000000000 3 -0.600000 -8.999999999999998 4 -0.600000 11.40000000000000 5 -0.600000 -2.519999999999995 0 -0.400000 0.000000000000000 1 -0.400000 0.000000000000000 2 -0.400000 3.000000000000000 3 -0.400000 -6.000000000000001 4 -0.400000 0.9000000000000012 5 -0.400000 10.92000000000000 0 -0.200000 0.000000000000000 1 -0.200000 0.000000000000000 2 -0.200000 3.000000000000000 3 -0.200000 -3.000000000000000 4 -0.200000 -5.399999999999999 5 -0.200000 9.239999999999998 0 0.000000 0.000000000000000 1 0.000000 0.000000000000000 2 0.000000 3.000000000000000 3 0.000000 0.000000000000000 4 0.000000 -7.500000000000000 5 0.000000 -0.000000000000000 0 0.200000 0.000000000000000 1 0.200000 0.000000000000000 2 0.200000 3.000000000000000 3 0.200000 3.000000000000000 4 0.200000 -5.399999999999999 5 0.200000 -9.239999999999998 0 0.400000 0.000000000000000 1 0.400000 0.000000000000000 2 0.400000 3.000000000000000 3 0.400000 6.000000000000001 4 0.400000 0.9000000000000012 5 0.400000 -10.92000000000000 0 0.600000 0.000000000000000 1 0.600000 0.000000000000000 2 0.600000 3.000000000000000 3 0.600000 8.999999999999998 4 0.600000 11.40000000000000 5 0.600000 2.519999999999995 0 0.800000 0.000000000000000 1 0.800000 0.000000000000000 2 0.800000 3.000000000000000 3 0.800000 12.00000000000000 4 0.800000 26.10000000000000 5 0.800000 38.64000000000001 0 1.000000 0.000000000000000 1 1.000000 0.000000000000000 2 1.000000 3.000000000000000 3 1.000000 15.00000000000000 4 1.000000 45.00000000000000 5 1.000000 105.0000000000000 P_POLYNOMIAL_VALUE_TEST: P_POLYNOMIAL_VALUE evaluates the Legendre polynomial P(n,x). Tabulated Computed N X P(N,X) P(N,X) Error 0 0.250000 1.000000000000000 1.000000000000000 0.0 1 0.250000 0.2500000000000000 0.2500000000000000 0.0 2 0.250000 -0.4062500000000000 -0.4062500000000000 0.0 3 0.250000 -0.3359375000000000 -0.3359375000000000 0.0 4 0.250000 0.1577148437500000 0.1577148437500000 0.0 5 0.250000 0.3397216796875000 0.3397216796875000 0.0 6 0.250000 0.2427673339843750E-01 0.2427673339843750E-01 0.0 7 0.250000 -0.2799186706542969 -0.2799186706542969 0.0 8 0.250000 -0.1524540185928345 -0.1524540185928345 -.28E-16 9 0.250000 0.1768244206905365 0.1768244206905365 0.0 10 0.250000 0.2212002165615559 0.2212002165615559 0.28E-16 3 0.000000 0.000000000000000 -0.000000000000000 0.0 3 0.100000 -0.1475000000000000 -0.1475000000000000 0.0 3 0.200000 -0.2800000000000000 -0.2800000000000000 0.0 3 0.300000 -0.3825000000000000 -0.3825000000000000 0.0 3 0.400000 -0.4400000000000000 -0.4399999999999999 -.56E-16 3 0.500000 -0.4375000000000000 -0.4375000000000000 0.0 3 0.600000 -0.3600000000000000 -0.3600000000000000 0.56E-16 3 0.700000 -0.1925000000000000 -0.1925000000000001 0.11E-15 3 0.800000 0.8000000000000000E-01 0.8000000000000022E-01 -.22E-15 3 0.900000 0.4725000000000000 0.4725000000000001 -.11E-15 3 1.000000 1.000000000000000 1.000000000000000 0.0 P_POLYNOMIAL_ZEROS_TEST: P_POLYNOMIAL_ZEROS computes the zeros of P(n,x) Check by calling P_POLYNOMIAL_VALUE. Computed zeros for P(1,z): 1: 0.0000000 Evaluate P(1,z): 1: 0.0000000 Computed zeros for P(2,z): 1: -0.57735027 2: 0.57735027 Evaluate P(2,z): 1: -0.27755576E-15 2: -0.27755576E-15 Computed zeros for P(3,z): 1: -0.77459667 2: 0.19949320E-16 3: 0.77459667 Evaluate P(3,z): 1: 0.22204460E-15 2: -0.29923980E-16 3: -0.66613381E-15 Computed zeros for P(4,z): 1: -0.86113631 2: -0.33998104 3: 0.33998104 4: 0.86113631 Evaluate P(4,z): 1: 0.55511151E-15 2: 0.55511151E-16 3: 0.55511151E-16 4: -0.16653345E-15 Computed zeros for P(5,z): 1: -0.90617985 2: -0.53846931 3: -0.10818539E-15 4: 0.53846931 5: 0.90617985 Evaluate P(5,z): 1: -0.97699626E-15 2: -0.31086245E-15 3: -0.20284760E-15 4: -0.44408921E-16 5: -0.10658141E-14 P_POWER_PRODUCT_TEST P_POWER_PRODUCT_TEST computes a power product table for P(n,x): Tij = integral ( -1 <= x <= +1 ) x^e P(i,x) P(j,x) dx Maximum degree P = 5 Exponent of X, E = 0 Power product table: Col 1 2 3 4 5 Row 1: 2.00000 0.305311E-15 0.971445E-15 0.138778E-15 0.568989E-15 2: 0.305311E-15 0.666667 0.166533E-15 0.721645E-15 0.235922E-15 3: 0.971445E-15 0.166533E-15 0.400000 0.235922E-15 0.360822E-15 4: 0.138778E-15 0.749401E-15 0.222045E-15 0.285714 0.277556E-16 5: 0.568989E-15 0.235922E-15 0.374700E-15 0.138778E-16 0.222222 6: 0.319189E-15 0.201228E-15 0. 0.267147E-15 0.433681E-16 Col 6 Row 1: 0.319189E-15 2: 0.180411E-15 3: 0.346945E-17 4: 0.260209E-15 5: 0.503070E-16 6: 0.181818 P_POWER_PRODUCT_TEST P_POWER_PRODUCT_TEST computes a power product table for P(n,x): Tij = integral ( -1 <= x <= +1 ) x^e P(i,x) P(j,x) dx Maximum degree P = 5 Exponent of X, E = 1 Power product table: Col 1 2 3 4 5 Row 1: 0.915934E-15 0.666667 0.208167E-15 -0.360822E-15 -0.346945E-15 2: 0.666667 0.430211E-15 0.266667 -0.138778E-15 -0.374700E-15 3: 0.208167E-15 0.266667 0.138778E-16 0.171429 -0.277556E-15 4: -0.360822E-15 -0.138778E-15 0.171429 -0.166533E-15 0.126984 5: -0.346945E-15 -0.374700E-15 -0.263678E-15 0.126984 -0.138778E-16 6: -0.395517E-15 -0.423273E-15 -0.326128E-15 -0.971445E-16 0.101010 Col 6 Row 1: -0.395517E-15 2: -0.437150E-15 3: -0.326128E-15 4: -0.104083E-15 5: 0.101010 6: 0.277556E-16 P_QUADRATURE_RULE_TEST: P_QUADRATURE_RULE computes the quadrature rule associated with P(n,x) X W 1 -0.906180 0.236927 2 -0.538469 0.478629 3 -0.108185E-15 0.568889 4 0.538469 0.478629 5 0.906180 0.236927 Use the quadrature rule to estimate: Q = Integral ( -1 <= X < +1 ) X^E dx E Q_Estimate Q_Exact 0 2.00000 2.00000 1 0.277556E-16 0.00000 2 0.666667 0.666667 3 -0.138778E-15 0.00000 4 0.400000 0.400000 5 -0.222045E-15 0.00000 6 0.285714 0.285714 7 -0.249800E-15 0.00000 8 0.222222 0.222222 9 -0.249800E-15 0.00000 PM_POLYNOMIAL_VALUE_TEST: PM_POLYNOMIAL_VALUE evaluates the Legendre polynomial Pm(n,m,x). Tabulated Computed N M X Pm(N,M,X) Pm(N,M,X) Error 1 0 0.000000 0.000000000000000 0.000000000000000 0.0 2 0 0.000000 -0.5000000000000000 -0.5000000000000000 0.0 3 0 0.000000 0.000000000000000 -0.000000000000000 0.0 4 0 0.000000 0.3750000000000000 0.3750000000000000 0.0 5 0 0.000000 0.000000000000000 0.000000000000000 0.0 1 1 0.500000 -0.8660254037844386 -0.8660254037844386 0.0 2 1 0.500000 -1.299038105676658 -1.299038105676658 0.0 3 1 0.500000 -0.3247595264191645 -0.3247595264191645 0.0 4 1 0.500000 1.353164693413185 1.353164693413185 -.44E-15 3 0 0.200000 -0.2800000000000000 -0.2800000000000000 0.0 3 1 0.200000 1.175755076535925 1.175755076535925 -.44E-15 3 2 0.200000 2.880000000000000 2.880000000000000 0.0 3 3 0.200000 -14.10906091843111 -14.10906091843110 -.71E-14 4 2 0.250000 -3.955078125000000 -3.955078125000000 0.44E-15 5 2 0.250000 -9.997558593750000 -9.997558593750002 0.18E-14 6 3 0.250000 82.65311444100485 82.65311444100486 -.14E-13 7 3 0.250000 20.24442836815152 20.24442836815153 -.11E-13 8 4 0.250000 -423.7997531890869 -423.7997531890869 -.57E-13 9 4 0.250000 1638.320624828339 1638.320624828339 0.0 10 5 0.250000 -20256.87389227225 -20256.87389227226 0.36E-11 PMN_POLYNOMIAL_VALUE_TEST: PMN_POLYNOMIAL_VALUE evaluates the Legendre polynomial Pmn(n,m,x). Tabulated Computed N M X Pmn(N,M,X) Pmn(N,M,X) Error 0 0 0.500000 0.7071067811865475 0.7071067811865476 -.11E-15 1 0 0.500000 0.6123724356957945 0.6123724356957945 0.0 1 1 0.500000 -0.7500000000000000 -0.7499999999999999 -.11E-15 2 0 0.500000 -0.1976423537605237 -0.1976423537605237 0.28E-16 2 1 0.500000 -0.8385254915624211 -0.8385254915624212 0.11E-15 2 2 0.500000 0.7261843774138907 0.7261843774138906 0.11E-15 3 0 0.500000 -0.8184875533567997 -0.8184875533567997 0.0 3 1 0.500000 -0.1753901900050285 -0.1753901900050285 0.28E-16 3 2 0.500000 0.9606516343087123 0.9606516343087123 0.0 3 3 0.500000 -0.6792832849776299 -0.6792832849776300 0.11E-15 4 0 0.500000 -0.6131941618102092 -0.6131941618102091 -.11E-15 4 1 0.500000 0.6418623720763665 0.6418623720763665 0.0 4 2 0.500000 0.4716705890038619 0.4716705890038619 0.0 4 3 0.500000 -1.018924927466445 -1.018924927466445 0.0 4 4 0.500000 0.6239615396237876 0.6239615396237875 0.11E-15 5 0 0.500000 0.2107022704608181 0.2107022704608181 -.28E-16 5 1 0.500000 0.8256314721961969 0.8256314721961968 0.11E-15 5 2 0.500000 -0.3982651281554632 -0.3982651281554632 -.56E-16 5 3 0.500000 -0.7040399320721435 -0.7040399320721434 -.11E-15 5 4 0.500000 1.034723155272289 1.034723155272289 0.44E-15 5 5 0.500000 -0.5667412129155530 -0.5667412129155530 0.0 PMNS_POLYNOMIAL_VALUE_TEST: PMNS_POLYNOMIAL_VALUE evaluates the Legendre polynomial Pmns(n,m,x). Tabulated Computed N M X Pmns(N,M,X) Pmns(N,M,X) Error 0 0 0.500000 0.2820947917738781 0.2820947917738781 -.56E-16 1 0 0.500000 0.2443012559514600 0.2443012559514600 0.28E-16 1 1 0.500000 -0.2992067103010745 -0.2992067103010745 0.0 2 0 0.500000 -0.7884789131313000E-01 -0.7884789131313001E-01 0.14E-16 2 1 0.500000 -0.3345232717786446 -0.3345232717786445 -.56E-16 2 2 0.500000 0.2897056515173922 0.2897056515173921 0.56E-16 3 0 0.500000 -0.3265292910163510 -0.3265292910163510 0.0 3 1 0.500000 -0.6997056236064664E-01 -0.6997056236064664E-01 0.0 3 2 0.500000 0.3832445536624809 0.3832445536624809 -.56E-16 3 3 0.500000 -0.2709948227475519 -0.2709948227475519 0.56E-16 4 0 0.500000 -0.2446290772414100 -0.2446290772414100 -.28E-16 4 1 0.500000 0.2560660384200185 0.2560660384200185 0.0 4 2 0.500000 0.1881693403754876 0.1881693403754876 0.28E-16 4 3 0.500000 -0.4064922341213279 -0.4064922341213280 0.56E-16 4 4 0.500000 0.2489246395003027 0.2489246395003027 -.56E-16 5 0 0.500000 0.8405804426339820E-01 0.8405804426339822E-01 -.14E-16 5 1 0.500000 0.3293793022891428 0.3293793022891428 0.0 5 2 0.500000 -0.1588847984307093 -0.1588847984307093 0.28E-16 5 3 0.500000 -0.2808712959945307 -0.2808712959945307 0.0 5 4 0.500000 0.4127948151484925 0.4127948151484925 0.0 5 5 0.500000 -0.2260970318780046 -0.2260970318780046 0.28E-16 PN_PAIR_PRODUCT_TEST PN_PAIR_PRODUCT_TEST computes a pair product table for Pn(n,x): Tij = integral ( -1 <= x <= +1 ) Pn(i,x) Pn(j,x) dx The Pn(n,x) polynomials are orthonormal, so T should be the identity matrix. Maximum degree P = 5 Pair product table: Col 1 2 3 4 5 Row 1: 1.00000 0.277556E-15 0.999201E-15 0.166533E-15 0.874301E-15 2: 0.249800E-15 1.00000 0.333067E-15 0.174860E-14 0.666134E-15 3: 0.102696E-14 0.305311E-15 1.00000 0.666134E-15 0.119349E-14 4: 0.194289E-15 0.169309E-14 0.777156E-15 1.00000 0.277556E-16 5: 0.888178E-15 0.666134E-15 0.122125E-14 0.277556E-16 1.00000 6: 0.541234E-15 0.555112E-15 0. 0.116573E-14 0.194289E-15 Col 6 Row 1: 0.513478E-15 2: 0.638378E-15 3: 0.277556E-16 4: 0.116573E-14 5: 0.194289E-15 6: 1.00000 PN_POLYNOMIAL_COEFFICIENTS_TEST PN_POLYNOMIAL_COEFFICIENTS determines polynomial coefficients of Pn(n,x). P( 0,x) = 0.707107 P( 1,x) = 1.22474 * x P( 2,x) = 2.37171 * x^ 2 -0.790569 P( 3,x) = 4.67707 * x^ 3 -2.80624 * x P( 4,x) = 9.28078 * x^ 4 -7.95495 * x^ 2 0.795495 P( 5,x) = 18.4685 * x^ 5 -20.5206 * x^ 3 4.39726 * x P( 6,x) = 36.8085 * x^ 6 -50.1935 * x^ 4 16.7312 * x^ 2 -0.796722 P( 7,x) = 73.4291 * x^ 7 -118.616 * x^ 5 53.9164 * x^ 3 -5.99072 * x P( 8,x) = 146.571 * x^ 8 -273.599 * x^ 6 157.846 * x^ 4 -28.6992 * x^ 2 0.797200 P( 9,x) = 292.689 * x^ 9 -619.813 * x^ 7 433.869 * x^ 5 -111.248 * x^ 3 7.58512 * x P(10,x) = 584.646 * x^10 -1384.69 * x^ 8 1140.33 * x^ 6 -380.111 * x^ 4 43.8589 * x^ 2 -0.797435 PN_POLYNOMIAL_VALUE_TEST: PN_POLYNOMIAL_VALUE evaluates the normalized Legendre polynomial Pn(n,x). Tabulated Computed N X Pn(N,X) Pn(N,X) Error 0 0.250000 0.7071067811865475 0.7071067811865475 0.0 1 0.250000 0.3061862178478972 0.3061862178478972 -.56E-16 2 0.250000 -0.6423376497217020 -0.6423376497217020 0.0 3 0.250000 -0.6284815141846855 -0.6284815141846855 0.0 4 0.250000 0.3345637065282053 0.3345637065282053 -.56E-16 5 0.250000 0.7967179601799685 0.7967179601799685 0.0 6 0.250000 0.6189376866246124E-01 0.6189376866246124E-01 0.0 7 0.250000 -0.7665888509210890 -0.7665888509210890 0.0 8 0.250000 -0.4444760242953344 -0.4444760242953344 0.0 9 0.250000 0.5450094674858101 0.5450094674858101 0.0 10 0.250000 0.7167706229835538 0.7167706229835538 0.0 3 0.000000 0.000000000000000 -0.000000000000000 0.0 3 0.100000 -0.2759472322745781 -0.2759472322745781 0.0 3 0.200000 -0.5238320341483518 -0.5238320341483518 0.0 3 0.300000 -0.7155919752205163 -0.7155919752205163 0.0 3 0.400000 -0.8231646250902670 -0.8231646250902670 0.0 3 0.500000 -0.8184875533567997 -0.8184875533567997 0.0 3 0.600000 -0.6734983296193094 -0.6734983296193094 0.0 3 0.700000 -0.3601345234769920 -0.3601345234769920 0.56E-16 3 0.800000 0.1496662954709581 0.1496662954709581 0.56E-16 3 0.900000 0.8839665576253438 0.8839665576253438 0.0 3 1.000000 1.870828693386971 1.870828693386971 0.44E-15 LEGENDRE_POLYNOMIAL_TEST: Normal end of execution. 15 September 2021 8:27:07.385 AM