Incomplete Gamma Function
Lower and upper incomplete gamma function.
gammainc(x, a) incgam(x, a)
x |
positive real number. |
a |
real number. |
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.
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.
Directly converting Fortran code is often easier than translating Matlab code generated with f2matlab.
Zhang, Sh., and J. Jin (1996). Computation of Special Functions. Wiley-Interscience, New York.
gammainc( 1.5, 2) gammainc(-1.5, 2) incgam(3, 1.2) incgam(3, 0.5); incgam(3, -0.5)
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.