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Some integrals involving a general class of polynomials and the multivariable H-function

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dc.contributor.author Srivastava, H.M.
dc.contributor.author Garg, Mridula
dc.date.accessioned 2009-09-04T18:11:20Z
dc.date.available 2009-09-04T18:11:20Z
dc.date.copyright 1986 en
dc.date.issued 2009-09-04T18:11:20Z
dc.identifier.uri http://hdl.handle.net/1828/1728
dc.description.abstract Motivated by a recent work of A. Gueran [3], the authors establish two general integral formulas associated with the H-function of several variables, which was introduced and studied in a series of papers by H.M. Srivastava and R. Panda (cf., e.g., [12] and [13]; see also [10]). Each of these integral formulas involves a product of the multivariable H-function and a general class of polynomials with essentially arbitrary coefficients. By assigning suitable special values to these coefficients, the main results can be reduced to the corresponding integrals involving the classical orthogonal polynomials including, for example, Hermite, Jacobi [and, of course, Gegenbauer (or ultraspherical), Legendre, and Tchebycheff], and Laguerre polynomials, the Bessel polynomials considered by H.L. Krall and O. Frink [4], and such other classes of generalized hypergeometric polynomials as those studied earlier by RF. Brafman [1], H.W. Gould and A.T. Hopper [2], and M. Lahiri [5]. Furthermore, the multivariable H-function occurring in each of our main results can be reduced, under various special cases, to such simpler functions as the generalized Lauricella function of H.M. Srivastava and M.C. Daoust [9], which indeed includes (as its particular cases) a great many of the useful functions of hypergeometric type in one and more variables. A specimen of some of these interesting applications of our main integral formulas is presented briefly. en
dc.description.sponsorship NSERC Grant A7353 and the University Grants Commission of India en
dc.language.iso en en
dc.relation.ispartofseries DM-421-IR en
dc.title Some integrals involving a general class of polynomials and the multivariable H-function en
dc.type Technical Report en


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