Chu Hyp0f1 Hyp1f0 Hyp1f1 Hyp1f1r Hyp2f0 Hyp2f1 Lhyp1f1

Lhyp1f1() Function Lhyp1f1 ( A As  Double, B As  Double, Z As  Double, Sign As  Long, Optional Info As  Long  ) Logarithm of hypergeometric function ln|1F1(a; b; z)| Purpose This routine computes the logarithm of the hypergeometric function ln|1F1(a; b; z)|. Returns Double ln|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. [out] Sign Sign of hypergeometric function. = -1: Negative. = 1: Positive. [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 routine 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 routine may abnormally terminate if the magnitude of a is very large. Reference boost/math/special_functions