Abstract
The integrals evaluated are the products of multivariable Aleph-functions with algebraic functions, Jacobi polynomials, Legendre functions, Bessel-Maitland functions, and general class of polynomials. The main results of our paper are quite general in nature and competent at yielding a very large number of integrals involving polynomials and various special functions occurring in the problem of mathematical analysis and mathematical physics.
Highlights
Introduction and PreliminariesThroughout this paper, consider C, R, R+, Z−0, and N to be a set of complex numbers, positive real numbers, nonpositive integers, and positive integers, respectively
The main results of our paper are quite general in nature and competent at yielding a very large number of integrals involving polynomials and various special functions occurring in the problem of mathematical analysis and mathematical physics
The multivariable Aleph (א) function of several complex variables generalizes the multivariable I-function, recently studied by Sharma and Ahmad [1], which itself is a generalization of G- and Hfunctions of multiple variables as
Summary
Throughout this paper, consider C, R, R+, Z−0 , and N to be a set of complex numbers, positive real numbers, nonpositive integers, and positive integers, respectively. The multivariable Aleph (א) function of several complex variables generalizes the multivariable I-function, recently studied by Sharma and Ahmad [1], which itself is a generalization of G- and Hfunctions of multiple variables as. By setting τi = τi(k) = 1, the multivariable Alephfunction reduces to multivariable I-function (see [1,2,3]]). = R(r) = 1, the multivariable Aleph-function reduces to multivariable H-function defined by Srivastava et al [4]. When we set r = 1, the multivariable Alephfunction reduces to Aleph-function of one variable defined by Südland [5].
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