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A new summation identity for the Srivastava-Singhal polynomials
Authors:Kung-Yu Chen
Institution:Department of Mathematics, Tamkang University, Tamsui 25137, Taiwan, Republic of China
Abstract:In his recent investigations involving differential operators for some generalizations of the classical Laguerre polynomials, H. Bavinck J. Phys. A Math. Gen. 29 (1996) L277-L279] encountered and proved a certain summation identity for the classical Laguerre polynomials. The main object of this sequel to Bavinck's work is to prove a generalization of this summation identity for the Srivastava-Singhal polynomials. The demonstration, which is presented here in the general case, differs markedly from the earlier proof given for the known special case. It is also indicated how the general summation identity can be applied to derive the corresponding result for one class of the Konhauser biorthogonal polynomials.
Keywords:Laguerre polynomials  Generating functions  Srivastava-Singhal polynomials  Stirling numbers of the second kind  Konhauser biorthogonal polynomials  Hermite polynomials
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