An Unified Study of Some Multiple Integrals with Multivariable Gimel-Function
multivariable gimel-function, multiple integral contours, a general class of polynomials, general finite multiple integral, generalized hypergeometric
Abstract
In this paper, we first evaluate a unified and general finite multiple integral whose integrand involves the product of the functions and the multivariable Gimel-function occurring in the integrand involve the product of factors of the form while that of occurring herein involves a finite series of such finite series of such factors. On account of the most general nature of the functions occurring in the integrand of our main integral, a large number of new and known integrals can easily be obtained from ot merely by specializing the functions and parameters involved therein. At the end of this study, we illustrate a new integral whose integrand involves a product of the Jacobi polynomial, the Appell's function and the Bessel function
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Frédéric Ayant (2016) An integral associated with Aleph-functions of several variables. 31(3), 142-154.
Frédéric Ayant (2018) An expansion formula for multivariable Gimel-function involving generalized Legendre Associated function. 56(4), 223-228.
B Braaksma (1962) Asymptotics expansions and analytic continuations for a class of Barnes-integrals. 15, 239-341.
K Gupta, R Jain (1993) A unified study of some multiple integrals. 19(1), 73-81.
Jagdish Prasad, Bhoopendra Verma (1986) Zooplankton Diversity in Didwana Lake: A Saline Lake in Rajasthan. 29(Of), 231-237.
J Prathima, V Nambisan, S Kurumujji (2014) A Study of I-function of Several Complex Variables. 1-12.
H Srivastava (1972) A class of integral equations involving the H function as kernel. 75(3), 212-220.
H Srivastava, K Gupta, S Goyal (1982) The H-function of one and two variables with applications.
H Srivastava, Pee Karlsson (1985) Multiple Gaussian hypergeometric serie.
H Srivastava, R Panda (1976) Some bilateral generating functions for a class of generalized hypergeometric polynomials.. 1976(283-284), 265-274.
A Gupta, D Kabe (1993) Some generalized multiple integrals involving zonal polynomials. 15(3), 299-303.
H Srivastava, R Panda (1976) Some expansion theorems and generating relations for the H-function of several complex variables II. 25, 167-197.
H Srivastava, N Singh (1983) The integration of certain products of the multivariableH-function with a general class of polynomials. 32(2), 157-187.
H Srivastava, Rekha Panda (1975) Some analytic or asymptotic confluent expansions for functions of several variables. 29(132), 1115-1128.
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2018-08-10
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