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Mathematics of Computation

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A unified presentation of certain classical polynomials

Authors: H. M. Srivastava and J. P. Singhal
Journal: Math. Comp. 26 (1972), 969-975
MSC: Primary 33A65
MathSciNet review: 0313560
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Abstract: This paper attempts to present a unified treatment of the classical orthogonal polynomials, viz. Jacobi, Laguerre and Hermite polynomials, and their generalizations introduced from time to time. The results obtained here include a number of linear, bilinear and bilateral generating functions and operational formulas for the polynomials $\{ T_n^{(\alpha ,\beta )}(x,a,b,c,d,p,r)|n = 0,1,2, \cdots \}$, defined by Eq. (3) below.*

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Keywords: Linear, bilinear and bilateral generating functions, orthogonal polynomials, Jacobi polynomials, Laguerre polynomials, Hermite polynomials, operational formulas, Bessel polynomials, Lagrange’s theorem, Gegenbauer polynomials, Leibniz’ rule, Taylor’s theorem
Article copyright: © Copyright 1972 American Mathematical Society