# Incomplete Gamma Function

### Description

Lower and upper incomplete gamma function.

### Usage

 1 gammainc(x, a) 

### Arguments

 x real number, not too big. a real positive number.

### Details

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).

Accuracy is 7 significant digits along the real axis.

### Value

Returns a list with the values of the lower, the upper, and regularized lower incomplete 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.

gamma
 1 2 gammainc( 1.5, 2) gammainc(-1.5, 2)