chu hyp0f1 hyp1f0 hyp1f1 hyp1f1r hyp2f0 hyppfq lhyp1f1

hyp1f1r() double hyp1f1r ( double  a, double  b, double  z  ) Regularized hypergeometric functions 1F1(a; b; z)/Γ(b) Purpose hyp1f1r computes the regularized hypergeometric function. 1F1(a; b; z)/Γ(b) = Σ(a)n * z^n / Γ(b + n) * n! (n = 0 to ∞) Returns 1F1(a; b; z)/Γ(b). Parameters [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. Error handling If a is not an integer with b < a <= 0 and b is a negative integer or zero, domain error (EDOM) occurs. Range error (ERANGE) may occur. Known issues Problem domains that are still unsolved for this routine exist as follows. Range error (ERANGE) may be reported 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. Reference boost/math/special_functions