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Index transforms associated with generalized hypergeometric functions

✍ Scribed by Semyon B. Yakubovich

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
117 KB
Volume
27
Category
Article
ISSN
0170-4214

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✦ Synopsis

We deal with a class of integral transformations whose kernels contain the Clausenian hypergeometric function 3 F 2 (a 1 ; a 2 ; a 3 ; b 1 ; b 2 ; z). These transforms are deΓΏned in terms of integrals with respect to their parameters. It involves as particular cases the familiar Olevskii and generalized Mehler-Fock transforms which are key tools in the methods of the mathematical theory of elasticity. The main theorem of boundedness of these operators as a map of L 2 (R+) β†’ L 2 (R+; x -1 dx) is proved. Some examples of the Olevskii and Mehler-Fock type integrals are given.

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We prove a Mehler representation for Jacobi functions t with respect to the dual variable . We exploit this representation to define a pair of dual integral transforms and its transposed t . We define two second order difference . operators P and Q such that t is an eigenfunction of P with respect

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## Abstract This paper deals with a class of integral transforms of the non ‐ convolution type involving sufficiently general kernels, which depend upon two essentially independent arguments. One of them, in various particular cases, is a parameter or index of the corresponding special functions. T