WChu WHyp0f1 WHyp1f0 WHyp1f1 WHyp1f1r WHyp2f0 WHyp2f1 WLhyp1f1

WHyp1f1() Function WHyp1f1 ( A As  Double, B As  Double, Z As  Double  ) Hypergeometric function 1F1(a; b; z) (Kummer's function M(a, b, z)) Purpose This function computes the hypergeometric function 1F1(a; b; z). 1F1(a; b; z) = M(a, b, z) = Σ(a)n * z^n / (b)n * n! (n = 0 to ∞) where M(a, b, z) is Kummer's function. Returns 1F1(a; b; z). 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. Note Problem domains that are still unsolved for this function exist as follows. Range error 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 function may abnormally terminate if the magnitude of a is very large. Reference boost/math/special_functions