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Eulerian and Other Integral Representations for Some Families of Hypergeometric Polynomials

H. M. Srivastava

Abstract


In the present contribution to the Special Volume dedicated to the Tricentennial Birthday Anniversary of Leonhard Euler (1707-1783), the author systematically investigates several general families of hypergeometric polynomials and their associated single-, double-, and triple-integral representations of the Eulerian and other types. Some interesting consequences of the general results presented here, involving such classical orthogonal polynomials as the Jacobi, Laguerre, Hermite, and Bessel polynomials, and also various other relatively less familiar hypergeometric polynomials such as (for example) the Konhauser-Toscano and Gould-Hopper polynomials, are also considered. Each of the many classesof integral representations, which are presented in this article, may be viewed also as a potentially useful linearization relationship for the product of two different members of the associated family of hypergeometric polynomials.

Keywords


Eulerian Beta integral, Integral representations, linearization relationships, Jacobi polynomials, Laguerre polynomials, Bessel polynomials, Hermite polynomials, hypergeometric functions and polynomials, Laplace and inverse Laplace transforms, Kampe de Feriet’s function, multivariable hypergeometric polynomials, Konhauser-Toscano polynomials,Gould-Hopper polynomials.

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