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 January 15, 2025)
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The power collection method for connection relations: Meixner polynomials
Published
Author(s)
, 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
Pub Type
Journals
Download Paper
Keywords
Generating functions, Connection coefficients, Connection-type relations, Eigenfunction expansions, Definite integrals, Infinite series
Citation
Issues
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Created November 7, 2017, Updated May 4, 2021