1
Gamma Functions, Beta Functions, and Related
Abstract
Topics of this chapter are gamma functions, beta functions, and related
functions in the complex domain. The evaluations are based on various
numerical techniques in dependence of the function argument. Related
functions are the Pochhammer symbol, the psi or digamma function, the
incomplete gamma function and its first and second derivative, the inverse
incomplete gamma function, and the incomplete beta function. In addition
some examples are discussed. Corresponding programming code can be
downloaded.
This chapter focuses on gamma functions and beta functions and related functions,
such as their derivatives and incomplete gamma respectively incomplete beta
functions. Γ - and β-functions are related to many special functions, integrals
and series expansions of differential equations and quite frequently used for
evaluation.
We will start with a short overview of relevant MATLAB- and toolbox functions.
1.1
Function Overview
Gamma function and related
• gamma MATLAB-function returns the gamma function restricted to real
arguments.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
W. Schweizer, Special Functions in Physics with MATLAB,
https://doi.org/10.1007/978-3-030-64232-7_1
1
Gamma Functions, Beta Functions, and Related
Abstract
Topics of this chapter are gamma functions, beta functions, and related
functions in the complex domain. The evaluations are based on various
numerical techniques in dependence of the function argument. Related
functions are the Pochhammer symbol, the psi or digamma function, the
incomplete gamma function and its first and second derivative, the inverse
incomplete gamma function, and the incomplete beta function. In addition
some examples are discussed. Corresponding programming code can be
downloaded.
This chapter focuses on gamma functions and beta functions and related functions,
such as their derivatives and incomplete gamma respectively incomplete beta
functions. Γ - and β-functions are related to many special functions, integrals
and series expansions of differential equations and quite frequently used for
evaluation.
We will start with a short overview of relevant MATLAB- and toolbox functions.
1.1
Function Overview
Gamma function and related
• gamma MATLAB-function returns the gamma function restricted to real
arguments.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
W. Schweizer, Special Functions in Physics with MATLAB,
https://doi.org/10.1007/978-3-030-64232-7_1
1