## File: Incomplete-Gamma-Functions.html

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 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108  GNU Scientific Library – Reference Manual: Incomplete Gamma Functions

7.19.4 Incomplete Gamma Functions

Function: double gsl_sf_gamma_inc (double a, double x)
Function: int gsl_sf_gamma_inc_e (double a, double x, gsl_sf_result * result)

These functions compute the unnormalized incomplete Gamma Function \Gamma(a,x) = \int_x^\infty dt t^{a-1} \exp(-t) for a real and x >= 0.

Function: double gsl_sf_gamma_inc_Q (double a, double x)
Function: int gsl_sf_gamma_inc_Q_e (double a, double x, gsl_sf_result * result)

These routines compute the normalized incomplete Gamma Function Q(a,x) = 1/\Gamma(a) \int_x^\infty dt t^{a-1} \exp(-t) for a > 0, x >= 0.

Function: double gsl_sf_gamma_inc_P (double a, double x)
Function: int gsl_sf_gamma_inc_P_e (double a, double x, gsl_sf_result * result)

These routines compute the complementary normalized incomplete Gamma Function P(a,x) = 1 - Q(a,x) = 1/\Gamma(a) \int_0^x dt t^{a-1} \exp(-t) for a > 0, x >= 0.

Note that Abramowitz & Stegun call P(a,x) the incomplete gamma function (section 6.5).