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An Algebraic Approach to Degenerate Appell Polynomials and Their Hybrid Forms via Determinants

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Abstract

It is remarkable that studying degenerate versions of polynomials from algebraic point of view is not limited to only special polynomials but can also be extended to their hybrid polynomials. Indeed for the first time, a closed determinant expression for the degenerate Appell polynomials is derived. The determinant forms for the degenerate Bernoulli and Euler polynomials are also investigated. A new class of the degenerate Hermite-Appell polynomials is investigated and some novel identities for these polynomials are established. The degenerate Hermite-Bernoulli and degenerate Hermite-Euler polynomials are considered as special cases of the degenerate Hermite-Appell polynomials. Further, by using Mathematica, we draw graphs of degenerate Hermite-Bernoulli polynomials for different values of indices. The zeros of these polynomials are also explored and their distribution is presented.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Engineering and Technology, Aligarh Muslim University, Aligarh, India

    Mumtaz Riyasat

  2. Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh, India

    Tabinda Nahid & Subuhi Khan

Authors
  1. Mumtaz Riyasat
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  2. Tabinda Nahid
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  3. Subuhi Khan
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Correspondence to Mumtaz Riyasat.

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Riyasat, M., Nahid, T. & Khan, S. An Algebraic Approach to Degenerate Appell Polynomials and Their Hybrid Forms via Determinants. Acta Math Sci 43, 719–735 (2023). https://doi.org/10.1007/s10473-023-0215-3

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  • DOI: https://doi.org/10.1007/s10473-023-0215-3

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