incomplete_gamma_lower Function

public pure elemental function incomplete_gamma_lower(a, x) result(rst)

Computes the lower incomplete gamma function.

The lower incomplete gamma function is defined as: $$\gamma(a, x) = \int_{0}^{x} t^{a-1} e^{-t} \,dt$$

Remarks

The value overflows for arguments beyond roughly $a = 171$, where $\Gamma(a)$ itself exceeds the range of a double precision number. Use regularized_gamma_lower where only the ratio to $\Gamma(a)$ is required.

See Also

• Wikipedia

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in)			::	a	The coefficient value.
real(kind=real64),	intent(in)			::	x	The value at which to evaluate the function.

Return Value real(kind=real64)

The function value.