Abstract
The Selberg integral was an integral first evaluated by Selberg in 1944. The aim of the present paper is to estimate generalized Selberg integral. It involves the product of the general class of multivariable polynomials, multivariable I-function and modified multivariable H-function. The result is believed to be new and is capable of giving a large number of integrals involving a variety of functions and polynomials as its cases. We shall see several corollaries and particular cases at the end.
Highlights
The aim of the present paper is to 11 estimate generalized Selberg integral. It involves the product of the general class of multivariable polynomials, multivariable I-function and modified multivariable H-function
The Selberg integral is the following integral first evaluated by Selberg [6] in 1944 : where n is a positive integer, a, b and c are the complex number such that
We evaluate a generalized Selberg integral involving the product of the multivariable I-function defined by Prasad [4], modified multivariable Hfunction defined by Prasad and Singh [5] and class of multivariable polynomials defined by Srivastava [7]
Summary
Abstract- The Selberg integral was an integral first evaluated by Selberg in 1944. The aim of the present paper is to estimate generalized Selberg integral. The Selberg integral is the following integral first evaluated by Selberg [6] in 1944 : where n is a positive integer, a, b and c are the complex number such that (1.1). We evaluate a generalized Selberg integral involving the product of the multivariable I-function defined by Prasad [4], modified multivariable Hfunction defined by Prasad and Singh [5] and class of multivariable polynomials defined by Srivastava [7]. The modified H-function studied by Prasad and Singh [5] generalizes the multivariable H-function defined by Srivastava and Panda [8,9]. It is defined in term of multiple Mellin-Barnes types integral:.
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