A general class of generating functions of biorthogonal polynomials
University of Aden Journal of Natural and Applied Sciences,
Vol. 20 No. 2 (2016),
31-08-2016
Page 377-386
DOI:
https://doi.org/10.47372/uajnas.2016.n2.a12
Abstract
In this paper we have obtained a new and known general class of bilateral and bilinear generating functions involving modified Konhauser biorthogonal \(Y_s^α (x;k)\), modified Bessel \(Y_s^n (u)\) and Laguerre polynomials \(L_n^α (x)\) by group theoretic method. As in particular cases we have obtained bilinear and unilateral generating functions. Consequently we recover the result of Rainville, Srivastava Manocha and McBride [25, 29, 23] and notice that the result of Das and Chatterjea [13] is the particular case of our result.
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Biorthogonal polynomials, Laguerre polynomials, modified Bessel polynomials, Generating functions, Group theoretic-method
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