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A generalization of the Euler beta function and applications
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Ilia Lomidze
Published/Copyright:
June 6, 2011
Abstract
A generalization of the Euler beta function to the case of a multi-dimensional variable is defined. In this context, the original beta function is a function of a two-dimensional variable. An analogue of the Euler formula for this new function is derived for the case of a three-dimensional variable. Based on the derived formula, a number of relations for the Gauss hypergeometrical function are obtained. Moreover, the analytic formulae for some new integrals of special functions are obtained.
Received: 2009-01-12
Published Online: 2011-06-06
Published in Print: 2011-June
© de Gruyter 2011
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Keywords for this article
Hypergeometric function;
special functions;
integrals of special functions
Articles in the same Issue
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- On a relationship between absolutely nonmeasurable functions and Sierpiński–Zygmund functions
- Boundedness of weighted singular integral operators in grand Lebesgue spaces
- A generalization of the Euler beta function and applications
- Normality and shared values concerning differential polynomial
- Fixed point theorems for singlevalued and multivalued generalized contractions in metric spaces endowed with a graph
- About some geometric characteristics of the generalized Möbius–Listing surfaces
- Variation formulas of solution for a delay differential equation taking into account delay perturbation and the continuous initial condition
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