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A new result for hypergeometric polynomials

Authors: Kung-Yu Chen and H. M. Srivastava
Journal: Proc. Amer. Math. Soc. 133 (2005), 3295-3302
MSC (2000): Primary 33C05, 33C45; Secondary 11B73
Published electronically: May 4, 2005
MathSciNet review: 2161152
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Abstract: In some recent investigations involving differential operators for generalized Laguerre polynomials, Herman Bavinck (1996) encountered and proved a certain summation formula for the classical Laguerre polynomials. The main object of this sequel to Bavinck's work is to prove a generalization of this summation formula for a class of hypergeometric polynomials. The demonstration, which is presented here in the general case, differs markedly from the earlier proof given for the known special case. The general summation formula is also applied to derive the corresponding result for the classical Jacobi polynomials.

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Additional Information

Kung-Yu Chen
Affiliation: Department of Mathematics, Tamkang University, Tamsui 25137, Taiwan, Republic of China

H. M. Srivastava
Affiliation: Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3P4, Canada

Keywords: Laguerre polynomials, generating functions, hypergeometric polynomials, Stirling numbers of the second kind, Jacobi polynomials, summation formula
Received by editor(s): February 26, 2004
Received by editor(s) in revised form: June 15, 2004
Published electronically: May 4, 2005
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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