13 September 2021 8:51:22.713 AM HERMITE_POLYNOMIAL_TEST: FORTRAN90 version. Test the HERMITE_POLYNOMIAL library. HERMITE_POLYNOMIAL_TEST01: H_POLYNOMIAL_VALUES stores values of the physicist's Hermite polynomials. H_POLYNOMIAL_VALUE evaluates the polynomial. Tabulated Computed N X H(N,X) H(N,X) Error 0 5.000000 1.000000000000000 1.000000000000000 0.0 1 5.000000 10.00000000000000 10.00000000000000 0.0 2 5.000000 98.00000000000000 98.00000000000000 0.0 3 5.000000 940.0000000000000 940.0000000000000 0.0 4 5.000000 8812.000000000000 8812.000000000000 0.0 5 5.000000 80600.00000000000 80600.00000000000 0.0 6 5.000000 717880.0000000000 717880.0000000000 0.0 7 5.000000 6211600.000000000 6211600.000000000 0.0 8 5.000000 52065680.00000000 52065680.00000000 0.0 9 5.000000 421271200.0000000 421271200.0000000 0.0 10 5.000000 3275529760.000000 3275529760.000000 0.0 11 5.000000 24329873600.00000 24329873600.00000 0.0 12 5.000000 171237081280.0000 171237081280.0000 0.0 5 0.000000 0.000000000000000 0.000000000000000 0.0 5 0.500000 41.00000000000000 41.00000000000000 0.0 5 1.000000 -8.000000000000000 -8.000000000000000 0.0 5 3.000000 3816.000000000000 3816.000000000000 0.0 5 10.000000 3041200.000000000 3041200.000000000 0.0 HERMITE_POLYNOMIAL_TEST02: HE_POLYNOMIAL_VALUES stores values of the probabilist's Hermite polynomials. HE_POLYNOMIAL_VALUE evaluates the polynomial. Tabulated Computed N X He(N,X) He(N,X) Error 0 5.000000 1.000000000000000 1.000000000000000 0.0 1 5.000000 5.000000000000000 5.000000000000000 0.0 2 5.000000 24.00000000000000 24.00000000000000 0.0 3 5.000000 110.0000000000000 110.0000000000000 0.0 4 5.000000 478.0000000000000 478.0000000000000 0.0 5 5.000000 1950.000000000000 1950.000000000000 0.0 6 5.000000 7360.000000000000 7360.000000000000 0.0 7 5.000000 25100.00000000000 25100.00000000000 0.0 8 5.000000 73980.00000000000 73980.00000000000 0.0 9 5.000000 169100.0000000000 169100.0000000000 0.0 10 5.000000 179680.0000000000 179680.0000000000 0.0 11 5.000000 -792600.0000000000 -792600.0000000000 0.0 12 5.000000 -5939480.000000000 -5939480.000000000 0.0 5 0.000000 0.000000000000000 0.000000000000000 0.0 5 0.500000 6.281250000000000 6.281250000000000 0.0 5 1.000000 6.000000000000000 6.000000000000000 0.0 5 3.000000 18.00000000000000 18.00000000000000 0.0 5 10.000000 90150.00000000000 90150.00000000000 0.0 HERMITE_POLYNOMIAL_TEST03: HF_FUNCTION_VALUES stores values of the Hermite function Hf(n,x). HF_FUNCTION_VALUE evaluates the function. Tabulated Computed N X Hf(N,X) Hf(N,X) Error 0 0.000000 0.7511255444649425 0.7511255444649425 0.0 1 0.000000 0.000000000000000 0.000000000000000 0.0 2 0.000000 -0.5311259660135985 -0.5311259660135984 -.11E-15 3 0.000000 0.000000000000000 -0.000000000000000 0.0 4 0.000000 0.4599685791773266 0.4599685791773266 0.0 5 0.000000 0.000000000000000 0.000000000000000 0.0 0 1.000000 0.4555806720113325 0.4555806720113325 0.0 1 1.000000 0.6442883651134752 0.6442883651134752 0.0 2 1.000000 0.3221441825567376 0.3221441825567377 -.56E-16 3 1.000000 -0.2630296236233334 -0.2630296236233334 0.56E-16 4 1.000000 -0.4649750762925110 -0.4649750762925110 0.0 5 1.000000 -0.5881521185179581E-01 -0.5881521185179584E-01 0.35E-16 6 1.000000 0.3905052515434106 0.3905052515434106 0.0 7 1.000000 0.2631861423064045 0.2631861423064046 -.56E-16 8 1.000000 -0.2336911435996523 -0.2336911435996523 0.0 9 1.000000 -0.3582973361472840 -0.3582973361472841 0.11E-15 10 1.000000 0.6146344487883041E-01 0.6146344487883037E-01 0.42E-16 11 1.000000 0.3678312067984882 0.3678312067984882 -.56E-16 12 1.000000 0.9131969309166278E-01 0.9131969309166282E-01 -.42E-16 5 0.500000 0.4385750950032321 0.4385750950032322 -.56E-16 5 2.000000 -0.2624689527931006E-01 -0.2624689527930978E-01 -.28E-15 5 3.000000 0.5138426125477819 0.5138426125477823 -.44E-15 5 4.000000 0.9355563118061758E-01 0.9355563118061762E-01 -.42E-16 HERMITE_POLYNOMIAL_TEST04: H_POLYNOMIAL_ZEROS computes the zeros of H(n,x) Check by calling H_POLYNOMIAL there. Computed zeros for H(1,z): 1: 0.0000000 Evaluate H(1,z): 1: 0.0000000 Computed zeros for H(2,z): 1: -0.70710678 2: 0.70710678 Evaluate H(2,z): 1: -0.44408921E-15 2: -0.44408921E-15 Computed zeros for H(3,z): 1: -1.2247449 2: -0.98628450E-16 3: 1.2247449 Evaluate H(3,z): 1: -0.88817842E-14 2: 0.11835414E-14 3: 0.88817842E-14 Computed zeros for H(4,z): 1: -1.6506801 2: -0.52464762 3: 0.52464762 4: 1.6506801 Evaluate H(4,z): 1: -0.10658141E-12 2: -0.88817842E-15 3: 0.26645353E-14 4: -0.42632564E-13 Computed zeros for H(5,z): 1: -2.0201829 2: -0.95857246 3: 0.24025794E-15 4: 0.95857246 5: 2.0201829 Evaluate H(5,z): 1: 0.0000000 2: -0.21316282E-13 3: 0.28830953E-13 4: -0.42632564E-13 5: 0.0000000 HERMITE_POLYNOMIAL_TEST05: HE_POLYNOMIAL_ZEROS computes the zeros of He(n,x) Check by calling HE_POLYNOMIAL there. Computed zeros for He(1,z): 1: 0.0000000 Evaluate He(1,z): 1: 0.0000000 Computed zeros for He(2,z): 1: -1.0000000 2: 1.0000000 Evaluate He(2,z): 1: 0.0000000 2: 0.0000000 Computed zeros for He(3,z): 1: -1.7320508 2: -0.13948169E-15 3: 1.7320508 Evaluate He(3,z): 1: -0.31086245E-14 2: 0.41844507E-15 3: 0.31086245E-14 Computed zeros for He(4,z): 1: -2.3344142 2: -0.74196378 3: 0.74196378 4: 2.3344142 Evaluate He(4,z): 1: -0.19539925E-13 2: -0.44408921E-15 3: 0.44408921E-15 4: -0.88817842E-14 Computed zeros for He(5,z): 1: -2.8569700 2: -1.3556262 3: 0.33977604E-15 4: 1.3556262 5: 2.8569700 Evaluate He(5,z): 1: 0.14210855E-13 2: -0.35527137E-14 3: 0.50966406E-14 4: -0.11546319E-13 5: -0.14210855E-13 HERMITE_POLYNOMIAL_TEST06: H_QUADRATURE_RULE computes the quadrature rule associated with H(n,x) X W 1 -2.65196 0.971781E-03 2 -1.67355 0.545156E-01 3 -0.816288 0.425607 4 -0.105979E-15 0.810265 5 0.816288 0.425607 6 1.67355 0.545156E-01 7 2.65196 0.971781E-03 Use the quadrature rule to estimate: Q = Integral ( -oo < X < +00 ) X^E exp(-X^2) dx E Q_Estimate Q_Exact 0 1.77245 1.77245 1 0.347378E-15 0.00000 2 0.886227 0.886227 3 0.544703E-15 0.00000 4 1.32934 1.32934 5 0.174860E-14 0.00000 6 3.32335 3.32335 7 0.643929E-14 0.00000 8 11.6317 11.6317 9 0.293099E-13 0.00000 10 52.3428 52.3428 11 0.142109E-12 0.00000 12 287.885 287.885 13 0.738964E-12 0.00000 HERMITE_POLYNOMIAL_TEST07: HE_QUADRATURE_RULE computes the quadrature rule associated with He(n,x) X W 1 -3.75044 0.137431E-02 2 -2.36676 0.770967E-01 3 -1.15441 0.601900 4 -0.149876E-15 1.14589 5 1.15441 0.601900 6 2.36676 0.770967E-01 7 3.75044 0.137431E-02 Use the quadrature rule to estimate: Q = Integral ( -oo < X < +00 ) X^E exp(-0.5*X^2) dx E Q_Estimate Q_Exact 0 2.50663 2.50663 1 0.695624E-15 0.00000 2 2.50663 2.50663 3 0.219269E-14 0.00000 4 7.51988 7.51988 5 0.108802E-13 0.00000 6 37.5994 37.5994 7 0.781597E-13 0.00000 8 263.196 263.196 9 0.625278E-12 0.00000 10 2368.76 2368.76 11 0.727596E-11 0.00000 12 26056.4 26056.4 13 0.873115E-10 0.00000 HERMITE_POLYNOMIAL_TEST08 Compute a normalized physicist's Hermite exponential product table. Tij = integral ( -oo < X < +oo ) exp(B*X) Hn(I,X) Hn(J,X) exp(-X*X) dx where Hn(I,X) = normalized physicist's Hermite polynomial of degree I. Maximum degree P = 5 Exponential argument coefficient B = 0.00000 Exponential product table: Col 1 2 3 4 5 Row 1: 1.00000 0.434968E-15 0.760568E-15 -0.561617E-16 -0.398986E-16 2: 0.434968E-15 1.00000 0.462521E-15 0.129540E-14 -0.388578E-15 3: 0.760568E-15 0.427609E-15 1.00000 -0.520417E-16 0.725114E-15 4: -0.101156E-15 0.126722E-14 -0.242861E-16 1.00000 0.971445E-15 5: -0.121431E-16 -0.416334E-15 0.752870E-15 0.964506E-15 1.00000 6: -0.107987E-15 -0.697359E-15 0.534295E-15 0.166533E-15 -0.111022E-15 Col 6 Row 1: -0.941087E-16 2: -0.667869E-15 3: 0.548173E-15 4: 0.124900E-15 5: -0.111022E-15 6: 1.00000 HERMITE_POLYNOMIAL_TEST08 Compute a normalized physicist's Hermite exponential product table. Tij = integral ( -oo < X < +oo ) exp(B*X) Hn(I,X) Hn(J,X) exp(-X*X) dx where Hn(I,X) = normalized physicist's Hermite polynomial of degree I. Maximum degree P = 5 Exponential argument coefficient B = 1.00000 Exponential product table: Col 1 2 3 4 5 Row 1: 1.28403 0.907943 0.453972 0.185333 0.655251E-01 2: 0.907943 1.92604 1.60503 0.917352 0.416999 3: 0.453972 1.60503 2.72855 2.42443 1.50583 4: 0.185333 0.917352 2.42443 3.71832 3.41422 5: 0.655251E-01 0.416999 1.50583 3.41422 4.92527 6: 0.207208E-01 0.161169 0.739903 2.24593 4.61020 Col 6 Row 1: 0.207208E-01 2: 0.161169 3: 0.739903 4: 2.24593 5: 4.61020 6: 6.37677 HERMITE_POLYNOMIAL_TEST09 Compute a normalized physicist's Hermite power product table. Tij = integral ( -oo < X < +oo ) X^E Hn(I,X) Hn(J,X) exp(-X*X) dx where Hn(I,X) = normalized physicist's Hermite polynomial of degree I. Maximum degree P = 5 Exponent of X, E = 0 Power product table: Col 1 2 3 4 5 Row 1: 0. 0. 0.845591-308 0.197559-307 0.372537-307 2: 0. 0. 0. 0. 0. 3: 0.845591-308 0. 187.499 438.063 826.055 4: 0.197559-307 0. 438.063 1023.47 1929.95 5: 0.372537-307 0. 826.055 1929.95 3639.30 6: 0.575137-307 0. 1275.30 2979.53 5618.50 Col 6 Row 1: 0.575137-307 2: 0. 3: 1275.30 4: 2979.53 5: 5618.50 6: 8674.06 HERMITE_POLYNOMIAL_TEST09 Compute a normalized physicist's Hermite power product table. Tij = integral ( -oo < X < +oo ) X^E Hn(I,X) Hn(J,X) exp(-X*X) dx where Hn(I,X) = normalized physicist's Hermite polynomial of degree I. Maximum degree P = 5 Exponent of X, E = 1 Power product table: Col 1 2 3 4 5 Row 1: 0. 0. 0. 0. 0. 2: 0. 0. 0. 0. 0. 3: 0.494066-323 0. 0.456302E-13 0.100808E-12 0.181410E-12 4: 0.988131-323 0. 0.100808E-12 0.248468E-12 0.439648E-12 5: 0.988131-323 0. 0.181410E-12 0.439204E-12 0.930811E-12 6: 0.988131-323 0. 0.272449E-12 0.612843E-12 0.138023E-11 Col 6 Row 1: 0. 2: 0. 3: 0.272449E-12 4: 0.726530E-12 5: 0.143707E-11 6: 0.203215E-11 HERMITE_POLYNOMIAL_TEST10 Compute a normalized probabilist's Hermite exponential product table. Tij = integral ( -oo < X < +oo ) exp(B*X) Hen(I,X) Hen(J,X) exp(-X*X) dx where Hen(I,X) = normalized probabilist's Hermite polynomial of degree I. Maximum degree P = 5 Exponential argument coefficient B = 0.00000 Exponential product table: Col 1 2 3 4 5 Row 1: 1.00000 0.393335E-15 0.843889E-15 -0.315503E-16 -0.706900E-16 2: 0.448846E-15 1.00000 0.518249E-15 0.147712E-14 -0.358220E-15 3: 0.913278E-15 0.573977E-15 1.00000 0.149186E-15 0.929812E-15 4: -0.626669E-16 0.147755E-14 0.204697E-15 1.00000 0.950628E-15 5: -0.672205E-16 -0.329597E-15 0.933281E-15 0.895117E-15 1.00000 6: -0.174773E-15 -0.794503E-15 0.291434E-15 0.138778E-16 -0.138778E-15 Col 6 Row 1: -0.174773E-15 2: -0.822259E-15 3: 0.249800E-15 4: 0. 5: -0.166533E-15 6: 1.00000 HERMITE_POLYNOMIAL_TEST10 Compute a normalized probabilist's Hermite exponential product table. Tij = integral ( -oo < X < +oo ) exp(B*X) Hen(I,X) Hen(J,X) exp(-X*X) dx where Hen(I,X) = normalized probabilist's Hermite polynomial of degree I. Maximum degree P = 5 Exponential argument coefficient B = 1.00000 Exponential product table: Col 1 2 3 4 5 Row 1: 1.64872 1.64872 1.16582 0.673087 0.336543 2: 1.64872 3.29744 3.49747 2.69235 1.68270 3: 1.16582 3.49747 5.77052 6.18726 4.99725 4: 0.673087 2.69235 6.18726 9.34255 10.0284 5: 0.336543 1.68270 4.99725 10.0284 14.3501 6: 0.150499 0.902934 3.29819 8.34976 15.3556 Col 6 Row 1: 0.150499 2: 0.902934 3: 3.29819 4: 8.34976 5: 15.3556 6: 21.0802 HERMITE_POLYNOMIAL_TEST11 Compute a normalized probabilist's Hermite power product table. Tij = integral ( -oo < X < +oo ) X^E Hen(I,X) Hen(J,X) exp(-X*X) dx where Hn(I,X) = normalized probabilist's Hermite polynomial of degree I. Maximum degree P = 5 Exponent of X, E = 0 Power product table: Col 1 2 3 4 5 Row 1: 1.00000 -0.647052E-15 -0.759809E-15 -0.277556E-16 0.437150E-15 2: -0.619296E-15 1.00000 -0.770217E-15 -0.457967E-15 -0.138778E-16 3: -0.732053E-15 -0.881240E-15 1.00000 -0.915934E-15 0.555112E-15 4: -0.277556E-16 -0.471845E-15 -0.915934E-15 1.00000 -0.155431E-14 5: 0.440620E-15 0.277556E-16 0.527356E-15 -0.155431E-14 1.00000 6: 0.693889E-17 0.943690E-15 -0.277556E-15 0.308087E-14 -0.555112E-15 Col 6 Row 1: 0.589806E-16 2: 0.971445E-15 3: -0.277556E-15 4: 0.305311E-14 5: -0.582867E-15 6: 1.00000 HERMITE_POLYNOMIAL_TEST11 Compute a normalized probabilist's Hermite power product table. Tij = integral ( -oo < X < +oo ) X^E Hen(I,X) Hen(J,X) exp(-X*X) dx where Hn(I,X) = normalized probabilist's Hermite polynomial of degree I. Maximum degree P = 5 Exponent of X, E = 1 Power product table: Col 1 2 3 4 5 Row 1: 0.317454E-15 1.00000 0.457967E-15 0.423273E-15 -0.117961E-15 2: 1.00000 0.891648E-15 1.41421 0.582867E-15 0.527356E-15 3: 0.426742E-15 1.41421 0.133227E-14 1.73205 0.943690E-15 4: 0.478784E-15 0.610623E-15 1.73205 0.188738E-14 2.00000 5: -0.902056E-16 0.610623E-15 0.943690E-15 2.00000 0.244249E-14 6: -0.215106E-15 0.832667E-16 -0.111022E-15 0.111022E-14 2.23607 Col 6 Row 1: -0.222045E-15 2: 0.277556E-16 3: -0.555112E-16 4: 0.111022E-14 5: 2.23607 6: 0.288658E-14 HERMITE_POLYNOMIAL_TEST12 Compute a Hermite function exponential product table. Tij = integral ( -oo < X < +oo ) exp(B*X) Hf(I,X) Hf(J,X) exp(-X*X) dx where Hf(I,X) = Hermite function of "degree" I. Maximum degree P = 5 Exponential argument coefficient B = 0.00000 Exponential product table: Col 1 2 3 4 5 Row 1: 1.00000 0.490466E-15 0.826487E-15 -0.385976E-16 0.331766E-16 2: 0.532113E-15 1.00000 0.622115E-15 0.146281E-14 -0.456232E-15 3: 0.829957E-15 0.629054E-15 1.00000 0.902056E-16 0.100961E-14 4: -0.109504E-16 0.147625E-14 0.624500E-16 1.00000 0.104777E-14 5: 0.227682E-16 -0.470110E-15 0.103736E-14 0.104777E-14 1.00000 6: -0.152656E-15 -0.631439E-15 0.419803E-15 0.235922E-15 -0.555112E-16 Col 6 Row 1: -0.152656E-15 2: -0.631439E-15 3: 0.433681E-15 4: 0.208167E-15 5: -0.832667E-16 6: 1.00000 HERMITE_POLYNOMIAL_TEST12 Compute a Hermite function exponential product table. Tij = integral ( -oo < X < +oo ) exp(B*X) Hf(I,X) Hf(J,X) exp(-X*X) dx where Hf(I,X) = Hermite function of "degree" I. Maximum degree P = 5 Exponential argument coefficient B = 1.00000 Exponential product table: Col 1 2 3 4 5 Row 1: 1.28403 0.907943 0.453972 0.185333 0.655251E-01 2: 0.907943 1.92604 1.60503 0.917352 0.416999 3: 0.453972 1.60503 2.72855 2.42443 1.50583 4: 0.185333 0.917352 2.42443 3.71832 3.41422 5: 0.655251E-01 0.416999 1.50583 3.41422 4.92527 6: 0.207208E-01 0.161169 0.739903 2.24593 4.61020 Col 6 Row 1: 0.207208E-01 2: 0.161169 3: 0.739903 4: 2.24593 5: 4.61020 6: 6.37677 HERMITE_POLYNOMIAL_TEST13 Compute a Hermite function power product table. Tij = integral ( -oo < X < +oo ) X^E Hf(I,X) Hf(J,X) exp(-X*X) dx where Hf(I,X) = Hermite function of "degree" I. Maximum degree P = 5 Exponent of X, E = 0 Power product table: Col 1 2 3 4 5 Row 1: 1.00000 -0.506539E-15 -0.902056E-15 -0.277556E-16 0.457967E-15 2: -0.534295E-15 1.00000 -0.950628E-15 -0.624500E-15 0.277556E-16 3: -0.846545E-15 -0.950628E-15 1.00000 -0.108247E-14 0.388578E-15 4: -0.208167E-16 -0.652256E-15 -0.108247E-14 1. -0.172085E-14 5: 0.447559E-15 0. 0.388578E-15 -0.160982E-14 1.00000 6: -0.138778E-16 0.102696E-14 -0.360822E-15 0.299760E-14 -0.832667E-15 Col 6 Row 1: 0.520417E-16 2: 0.102696E-14 3: -0.360822E-15 4: 0.299760E-14 5: -0.832667E-15 6: 1.00000 HERMITE_POLYNOMIAL_TEST13 Compute a Hermite function power product table. Tij = integral ( -oo < X < +oo ) X^E Hf(I,X) Hf(J,X) exp(-X*X) dx where Hf(I,X) = Hermite function of "degree" I. Maximum degree P = 5 Exponent of X, E = 1 Power product table: Col 1 2 3 4 5 Row 1: 0.111022E-15 0.707107 0.313985E-15 0.232453E-15 -0.208167E-16 2: 0.707107 0.610623E-15 1.00000 0.777156E-15 0.166533E-15 3: 0.313985E-15 1.00000 0.127676E-14 1.22474 0.610623E-15 4: 0.208167E-15 0.652256E-15 1.22474 0.149880E-14 1.41421 5: -0.346945E-16 0.222045E-15 0.610623E-15 1.41421 0.177636E-14 6: -0.624500E-16 -0.222045E-15 0. 0.555112E-15 1.58114 Col 6 Row 1: -0.902056E-16 2: -0.222045E-15 3: -0.555112E-16 4: 0.555112E-15 5: 1.58114 6: 0.266454E-14 HERMITE_POLYNOMIAL_TEST14 H_POLYNOMIAL_COEFFICIENTS determines the physicist's Hermite polynomial coefficients. H( 0,x) = 1.00000 H( 1,x) = 2.00000 * x H( 2,x) = 4.00000 * x^ 2 -2.00000 H( 3,x) = 8.00000 * x^ 3 -12.0000 * x H( 4,x) = 16.0000 * x^ 4 -48.0000 * x^ 2 12.0000 H( 5,x) = 32.0000 * x^ 5 -160.000 * x^ 3 120.000 * x H( 6,x) = 64.0000 * x^ 6 -480.000 * x^ 4 720.000 * x^ 2 -120.000 H( 7,x) = 128.000 * x^ 7 -1344.00 * x^ 5 3360.00 * x^ 3 -1680.00 * x H( 8,x) = 256.000 * x^ 8 -3584.00 * x^ 6 13440.0 * x^ 4 -13440.0 * x^ 2 1680.00 H( 9,x) = 512.000 * x^ 9 -9216.00 * x^ 7 48384.0 * x^ 5 -80640.0 * x^ 3 30240.0 * x H(10,x) = 1024.00 * x^10 -23040.0 * x^ 8 161280. * x^ 6 -403200. * x^ 4 302400. * x^ 2 -30240.0 HERMITE_POLYNOMIAL_TEST15 HE_POLYNOMIAL_COEFFICIENTS determines the probabilist's Hermite polynomial coefficients. He( 0,x) = 1.00000 He( 1,x) = 1.00000 * x He( 2,x) = 1.00000 * x^ 2 -1.00000 He( 3,x) = 1.00000 * x^ 3 -3.00000 * x He( 4,x) = 1.00000 * x^ 4 -6.00000 * x^ 2 3.00000 He( 5,x) = 1.00000 * x^ 5 -10.0000 * x^ 3 15.0000 * x He( 6,x) = 1.00000 * x^ 6 -15.0000 * x^ 4 45.0000 * x^ 2 -15.0000 He( 7,x) = 1.00000 * x^ 7 -21.0000 * x^ 5 105.000 * x^ 3 -105.000 * x He( 8,x) = 1.00000 * x^ 8 -28.0000 * x^ 6 210.000 * x^ 4 -420.000 * x^ 2 105.000 He( 9,x) = 1.00000 * x^ 9 -36.0000 * x^ 7 378.000 * x^ 5 -1260.00 * x^ 3 945.000 * x He(10,x) = 1.00000 * x^10 -45.0000 * x^ 8 630.000 * x^ 6 -3150.00 * x^ 4 4725.00 * x^ 2 -945.000 HERMITE_POLYNOMIAL_TEST: Normal end of execution. 13 September 2021 8:51:22.714 AM