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General-Appell Polynomials within the Context of Monomiality Principle

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  • Subuhi Khan
  • Nusrat Raza

Abstract

A general class of the 2-variable polynomials is considered, and its properties are derived. Further, these polynomials are used to introduce the 2-variable general-Appell polynomials (2VgAP). The generating function for the 2VgAP is derived, and a correspondence between these polynomials and the Appell polynomials is established. The differential equation, recurrence relations, and other properties for the 2VgAP are obtained within the context of the monomiality principle. This paper is the first attempt in the direction of introducing a new family of special polynomials, which includes many other new special polynomial families as its particular cases.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:ijanal:328032
    DOI: 10.1155/2013/328032
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    References listed on IDEAS

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    1. Gabriella Bretti & Pierpaolo Natalini & Paolo E. Ricci, 2004. "Generalizations of the Bernoulli and Appell polynomials," Abstract and Applied Analysis, Hindawi, vol. 2004, pages 1-11, January.
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    Cited by:

    1. Shahid Ahmad Wani & Khalil Hadi Hakami & Hamad Zogan, 2024. "Several Characterizations of the Generalized 1-Parameter 3-Variable Hermite Polynomials," Mathematics, MDPI, vol. 12(16), pages 1-14, August.
    2. Francesco Aldo Costabile & Maria Italia Gualtieri & Anna Napoli, 2021. "General Bivariate Appell Polynomials via Matrix Calculus and Related Interpolation Hints," Mathematics, MDPI, vol. 9(9), pages 1-29, April.
    3. Özat, Zeynep & Çekim, Bayram & Ali Özarslan, Mehmet, 2023. "Δω-Laguerre based Appell polynomials and their properties associated with some special polynomials," Applied Mathematics and Computation, Elsevier, vol. 459(C).

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    1. Francesco Aldo Costabile & Maria Italia Gualtieri & Anna Napoli, 2021. "General Bivariate Appell Polynomials via Matrix Calculus and Related Interpolation Hints," Mathematics, MDPI, vol. 9(9), pages 1-29, April.

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