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Special Function Inverse Series Pairs
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  • 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;
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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.
Special functions;Series Inverses;Linear Algebra;Matrix Inverses;Bernoulli and Euler Polynomials;Combinatorial Identities;
 Cited by
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