regularized_gamma_lower Function

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

Computes the regularized lower incomplete gamma function.

The regularized lower incomplete gamma function is defined as: $$P(a, x) = \frac{\gamma(a, x)}{\Gamma(a)}$$

Remarks

The function is evaluated by means of a series expansion for $x < a + 1$ and a continued fraction otherwise, both carried to convergence and formed in logarithmic space. The routine is therefore well-behaved for arbitrarily large arguments, unlike the unregularized forms whose values overflow.

See Also

• Wikipedia

Arguments

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

Return Value real(kind=real64)

The function value, which lies on the interval [0, 1].