Special Function Inverse Series Pairs

- Journal title : Kyungpook mathematical journal
- Volume 50, Issue 2, 2010, pp.177-193
- Publisher : Department of Mathematics, Kyungpook National University
- DOI : 10.5666/KMJ.2010.50.2.177

Title & Authors

Special Function Inverse Series Pairs

Alsardary, Salar Yaseen; Gould, Henry Wadsworth;

Alsardary, Salar Yaseen; Gould, Henry Wadsworth;

Abstract

Working with the various special functions of mathematical physics and applied mathematics we often encounter inverse relations of the type and , where 0, 1, 2,. Here , denote special polynomial functions, and , denote coefficients found by use of the orthogonal properties of and , or by skillful series manipulations. Typically and , the n-th Legendre polynomial. We give a collection of inverse series pairs of the type if and only if , each pair being based on some reasonably well-known special function. We also state and prove an interesting generalization of a theorem of Rainville in this form.

Keywords

Special functions;Series Inverses;Linear Algebra;Matrix Inverses;Bernoulli and Euler Polynomials;Combinatorial Identities;

Language

English

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