A generalization of the Euler beta function and applications

作者：Lomidze Ilia^*

来源：Georgian Mathematical Journal, 2011, 18(2): 271-298.

DOI：10.1515/GMJ.2011.0025

• Hypergeometric function
• special functions
• integrals of special functions

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.

• 出版日期2011