gammainc.RdLower and upper incomplete gamma function.
gammainc(x, a)
incgam(x, a)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.
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.
Zhang, Sh., and J. Jin (1996). Computation of Special Functions. Wiley-Interscience, New York.
Directly converting Fortran code is often easier than translating Matlab code generated with f2matlab.
gammainc( 1.5, 2)
#> lowinc uppinc reginc
#> 0.4421746 0.5578254 0.4421746
gammainc(-1.5, 2)
#> lowinc uppinc reginc
#> 3.240845 -2.240845 3.240845
incgam(3, 1.2)
#> [1] 0.06542143
incgam(3, 0.5); incgam(3, -0.5)
#> [1] 0.02535651
#> [1] 0.006776136