◆ hyp1f1()

Hypergeometric function 1F1(a; b; z) (Kummer's function M(a, b, z))

Purpose: hyp1f1 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.

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.