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The power collection method for connection relations: Meixner polynomials

Published

Author(s)

Howard Cohl, Michael Baeder, Roberto Costas-Santos, Wenqing Xu

Abstract

We use and derive connection and connection-type relations for Meixner and Krawtchouk polynomials. These relations are used to derive generalizations of generating functions for these orthogonal polynomials. The coefficients of these generalized generating functions are given in term of double hypergeometric functions. From these generalized generating functions, we derive corresponding infinite series expressions by using the orthogonality relations.
Citation
Journal of Classical Analysis
Volume
11

Keywords

Generating functions, Connection coefficients, Connection-type relations, Eigenfunction expansions, Definite integrals, Infinite series

Citation

Cohl, H. , Baeder, M. , Costas-Santos, R. and Xu, W. (2017), The power collection method for connection relations: Meixner polynomials, Journal of Classical Analysis, [online], https://doi.org/10.7153/jca-2017-11-08, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=919101 (Accessed May 27, 2024)

Issues

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Created November 7, 2017, Updated May 4, 2021