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Unification of Two‐Variable Family of Apostol‐Type Polynomials with Applications

Author

Listed:
  • Beih S. El-Desouky
  • Rabab S. Gomaa
  • Alia M. Magar

Abstract

In this paper, the two‐variable unified family of generalized Apostol‐type polynomials is introduced, and some implicit forms and general symmetry identities are derived. Also, we obtain new degenerate Apostol‐type numbers and polynomials constructed from the new 2‐variable unified family. We derive explicit formulae of polynomials and identities that include some special numbers and polynomials. In addition, a probabilistic representation of the new family and some statistical properties are obtained.

Suggested Citation

  • Beih S. El-Desouky & Rabab S. Gomaa & Alia M. Magar, 2022. "Unification of Two‐Variable Family of Apostol‐Type Polynomials with Applications," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:4514725
    DOI: 10.1155/2022/4514725
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    References listed on IDEAS

    as
    1. Kyung-Won Hwang & Cheon Seoung Ryoo, 2020. "Some Identities Involving Two-Variable Partially Degenerate Hermite Polynomials Induced from Differential Equations and Structure of Their Roots," Mathematics, MDPI, vol. 8(4), pages 1-17, April.
    2. Taekyun Kim & Dae San Kim & Han Young Kim & Jongkyum Kwon, 2020. "Some Identities of Degenerate Bell Polynomials," Mathematics, MDPI, vol. 8(1), pages 1-8, January.
    3. Subuhi Khan & Nusrat Raza, 2013. "General-Appell Polynomials within the Context of Monomiality Principle," International Journal of Analysis, Hindawi, vol. 2013, pages 1-11, February.
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