2
1 Gamma Functions, Beta Functions, and Related
• gammaC SPECFUNPHYS-class returns the gamma function for real and
complex arguments.
• gammaln MATLAB-function returns the logarithm of the gamma function for
positive real arguments.
• gammalnC SPECFUNPHYS-class returns the logarithm of the gamma
function for arbitrary complex arguments.
Pochhammer Symbol pochC, pochlnC SPECFUNPHYS-class, returns the value
of the Pochhammer Symbol, respectively, its logarithm for complex arguments.
psi or digamma function is the logarithmic derivative of the gamma function. The
MATLAB-function psi is restricted to positive real arguments, the SPECFUNPHYS-class psiC supports complex arguments.
Incomplete gamma function
• gammainc MATLAB-function returns the value of the incomplete gamma
function for real values of the integral boundary and positive real numbers in
the integrand.
• incgammaC SPECFUNPHYS-class returns the value of the incomplete gamma function for complex arguments.
• diincgammaC returns the first two derivatives of the incomplete gamma
function supporting complex arguments.
• invincgammaC computes the inverse incomplete gamma function in the
complex domain.
Beta function and related
• beta MATLAB-function returns the beta function restricted to positive real
arguments
• betaC SPECFUNPHYS-class returns the beta function for real and complex
arguments
• betaln MATLAB-function returns the logarithm of the beta function for
positive real arguments.
• betalnC SPECFUNPHYS-class returns the logarithm of the beta function for
arbitrary complex arguments.
Incomplete Beta function The MATLAB-function betainc returns the incomplete beta function. The limit of the integral is restricted to the interval [0, 1]
and the integral values to positive real numbers. The SPECFUNPHYS-class
incbetaC works for arbitrary complex arguments.