Chu Chu_sub Hyp0f1 Hyp0f1_sub Hyp1f0 Hyp1f0_sub Hyp1f1 Hyp1f1_sub Hyp1f1r Hyp1f1r_sub Hyp2f0 Hyp2f0_sub Hyp2f1 Hyp2f1_sub Hyppfq Lhyp1f1 Lhyp1f1_sub

Hyp1f1r_sub() Sub Hyp1f1r_sub ( Ret As  Double, A As  Double, B As  Double, Z As  Double, Optional Info As  Long  ) Regularized hypergeometric functions 1F1(a; b; z)/Γ(b) (Subroutine version) Purpose Computes the regularized hypergeometric function 1F1(a; b; z)/Γ(b). 1F1(a; b; z)/Γ(b) = Σ(a)n * z^n / Γ(b + n) * n! (n = 0 to ∞) Parameters [out] Ret The regularized hypergeometric function 1F1(a; b; z)/Γ(b). [in] A Argument a. [in] B Argument b. (must not be a negative integer or zero unless A is an integer with B < A <= 0) [in] Z Argument z. [out] Info (Optional) = 0: Successful exit. = -1: The argument A or B had an illegal value. (A is not an integer with B < A <= 0 and B is a negative integer or zero) = 1: Floating point range error. Note Problem domains that are still unsolved for this program exist as follows. Range error (Info = 1) may occur in those cases. 1F1(-a, -b, -z): a, b and z all large. 1F1(-a, -b, z): a < b, b > z, this is really the same domain as above. 1F1(a, -b, z): There is a gap in between methods where no reliable implementation is possible, the issue becomes much worse for a, b and z all large. 1F1(tiny a, b, -z): There are some values where either the series is non-convergent (most particularly for b < 0) or where the series becomes divergent after a few terms limiting the precision that can be achieved. This program may abnormally terminate if the magnitude of a is very large. Reference boost/math/special_functions