gamma(x): Gamma¶

Gamma function.

Declaration¶

Syntax¶

retval = gamma(x)
elemental real function gamma(x)

Arguments¶

x the input value must be of type real. It should not be zero or a negative integer.

Return values¶

The return value is of same type and kind as of x.

Description¶

gamma(x) computes \(\gamma(x)\). For positive, integer value of x, the Gamma function simplifies to factorial function:

\(\gamma(x) = (x-1)!\)

In general, if \(x > 0\):

\(\gamma(x) = \int_{0}^{\infty} e^{-t} dt\)

and if \(-n-1 < x < -n\) where n is an integer >= 0:

\(\gamma(x) = \int_{0}^{\infty}(e ^{-t} - \sum\limits_{k=0}^n \frac{(-t)^k}{k!} dt)\)

Types¶

Supported argument types is real.

interface gamma
    module procedure sgamma, dgamma
end interface

contains

elemental real(sp) function sgamma(x)
real(sp), intent(in) :: x
end function

elemental real(dp) function dgamma(x)
real(dp), intent(in) :: x
end function

Examples¶

program intrinsics_gamma
	print *, gamma(0.5)
	print *, gamma(1.0)
end program

Result:

1.77245
1.000