R: Incomplete Gamma Function

gammainc {pracma} | R Documentation

## 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

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

and

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

while the regularized incomplete gamma function is γ(x, a)/Γ(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)

[Package pracma version 2.0.4 Index]