gammainc {pracma}

Incomplete Gamma Function

Description

Lower and upper incomplete gamma function.

Usage

gammainc(x, a)

incgam(x, a)

Arguments

x

positive real number.

a

real number.

Details

gammainc computes the lower and upper incomplete gamma function, including the regularized gamma function. The lower and upper incomplete gamma functions are defined as

\gamma(x, a) = \int_0^x e^{-t} \, t^{a-1} \, dt

and

\Gamma(x, a) = \int_x^{\infty} e^{-t} \, t^{a-1} \, dt

while the regularized incomplete gamma function is \gamma(x, a)/\Gamma(a).

incgam (a name used in Pari/GP) computes the upper incomplete gamma function alone, applying the R function pgamma. The accuracy is thus much higher. It works for a >= -1, for even smaller values a recursion will give the result.

Value

gammainc returns a list with the values of the lower, the upper, and regularized lower incomplete gamma function. incgam only returns the value of the incomplete upper gamma function.

Note

Directly converting Fortran code is often easier than translating Matlab code generated with f2matlab.

References

Zhang, Sh., and J. Jin (1996). Computation of Special Functions. Wiley-Interscience, New York.

See Also

gamma, pgamma

Examples

gammainc( 1.5, 2)
gammainc(-1.5, 2)

incgam(3, 1.2)
incgam(3, 0.5); incgam(3, -0.5)