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Two-dimensional generalized gamma function and its applications

Artem M. Ponomarenko

Abstract

In this article, we present a new two-dimensional generalization of the gamma function based on the product of the one-dimensional generalized beta function and the one-dimensional generalized gamma function. As will become clear later, this generalization is also a generalization the famous formula that gives the connection between the classical gamma and beta functions. Next we present properties of this generalization, some series for the generalized beta function. As a practical application of the two-dimensional generalized gamma function, we will show how it can be used to represent a fairly wide class of double integrals in the form of functional series.

Two-dimensional generalized gamma function and its applications

Abstract

In this article, we present a new two-dimensional generalization of the gamma function based on the product of the one-dimensional generalized beta function and the one-dimensional generalized gamma function. As will become clear later, this generalization is also a generalization the famous formula that gives the connection between the classical gamma and beta functions. Next we present properties of this generalization, some series for the generalized beta function. As a practical application of the two-dimensional generalized gamma function, we will show how it can be used to represent a fairly wide class of double integrals in the form of functional series.
Paper Structure (2 sections, 163 equations)

This paper contains 2 sections, 163 equations.

Table of Contents

  1. Introduction of a two-dimensional generalization of the gamma function and study of its properties.
  2. Practical applications of the generalized two-dimensional gamma function for calculating double integrals, including those containing some special functions.