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Function std.mathspecial.gammaIncomplete

Regularized lower incomplete gamma function P(a,x)

real gammaIncomplete(
  real a,
  real x
) pure nothrow @nogc @safe;

Mathematically, P(a,x) = γ(a,x)/Γ(a), where γ(a,x) is the lower incomplete gamma function, γ(a,x) = ∫0xta-1e-tdt, a > 0, and x ≥ 0.

Parameters

NameDescription
a the shape parameter, must be positive
x the fraction of integration completion from below, must be non-negative

Returns

It returns P(a,x), an element of [0,1].

Special Values
a x gammaIncomplete(a, x)
negative NAN
< 0 NAN
positive 0 0
positive ∞ 1
+0 > 0 1
∞ (0, ∞) 0

See Also

gamma and gammaIncompleteCompl

Example

assert(isClose(gammaIncomplete(1, 1), 1 - 1/E));
writeln(gammaIncomplete(1, 0)); // 0
writeln(gammaIncomplete(1, real.infinity)); // 1
writeln(gammaIncomplete(+0., 1)); // 1
writeln(gammaIncomplete(real.infinity, 1)); // 0

Authors

Stephen L. Moshier (original C code). Conversion to D by Don Clugston

License

Boost License 1.0.