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Some Families of Generating Functions Associated with Orthogonal Polynomials and Other Higher Transcendental Functions

Author

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  • Hari Mohan Srivastava

    (Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
    Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan
    Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy)

Abstract

In this invited survey-cum-expository review article, we present a brief and comprehensive account of some general families of linear and bilinear generating functions which are associated with orthogonal polynomials and such other higher transcendental functions as (for example) hypergeometric functions and hypergeometric polynomials in one, two and more variables. Many of the results as well as the methods and techniques used for their derivations, which are presented here, are intended to provide incentive and motivation for further research on the subject investigated in this article.

Suggested Citation

  • Hari Mohan Srivastava, 2022. "Some Families of Generating Functions Associated with Orthogonal Polynomials and Other Higher Transcendental Functions," Mathematics, MDPI, vol. 10(20), pages 1-23, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3730-:d:938857
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    References listed on IDEAS

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    1. Paolo Emilio Ricci & Rekha Srivastava, 2022. "A Note on the Laguerre-Type Appell and Hypergeometric Polynomials," Mathematics, MDPI, vol. 10(11), pages 1-11, June.
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    Cited by:

    1. Anton E. Kulagin & Alexander V. Shapovalov, 2023. "Analytical Description of the Diffusion in a Cellular Automaton with the Margolus Neighbourhood in Terms of the Two-Dimensional Markov Chain," Mathematics, MDPI, vol. 11(3), pages 1-18, January.
    2. Hari Mohan Srivastava, 2022. "Higher Transcendental Functions and Their Multi-Disciplinary Applications," Mathematics, MDPI, vol. 10(24), pages 1-3, December.

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