# General Properties of Generalized Gamma-Functions

## DOI:

https://doi.org/10.20535/1810-0546.2016.4.62211## Keywords:

Generalized gamma-functions, Incomplete gamma-functions, Digamma-functions## Abstract

**Background. **The article is dedicated to studies of the main properties of new generalized gamma-functions, generalized incomplete gamma-functions, generalized digamma-functions for their best applications in applied sciences, for calculations of integrals which are absent in scientific literature.

**Objective.** Introduction and study of the basic properties of the new generalized gamma-functions, generalized incomplete gamma-functions, generalized digamma-functions and their applications.

**Methods.** We apply the following methods: the methods of the theory of functions of the real variable, the theory of the special functions, the theory of the mathematical physics, the methods of applied analysis.

**Results.** Some new forms of generalized gamma-functions, incomplete gamma-functions, digamma-functions are introduced. The main properties of these generalized special functions are explored. Examples of application of new generalized gamma-functions are given.

**Conclusions.**With the help of the

*r*-generalized confluent hypergeometric functions the new generalization of gamma-functions, incomplete gamma-functions, digamma-functions are introduced. The main properties of the new generalized special functions are explored, examples of application of these functions are given.

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