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Some properties of degenerate Sheffer sequences based on algebraic approach

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Abstract

The algebraic approach endeavor a dominant tool for investigating properties of special polynomials. The main objective of this paper is to survey briefly the properties and applications of the degenerate Sheffer sequences and corresponding hybrid forms via determinants. In this article, a determinant form for the degenerate Sheffer sequences is investigated as a function of degenerate polynomial sequences of binomial type. Determinant forms and other properties for some members including the degenerate Poisson-Charlier, Korobov and degenerate actuarial sequences are also obtained. Further, the multi-variable degenerate Hermite-Sheffer sequences are introduced via determinants. Finally, the numerical results showing the approximate solutions of degenerate members and their hybrid forms are mentioned. The distribution of zeros is depicted via graphs.

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Acknowledgements

The authors are thankful to the Reviewer(s) for its valuable comments and suggestions towards the improvement of paper.

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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, Aligarh Muslim University, Aligarh, India

    Mehnaz Haneef & Subuhi Khan

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  1. Mumtaz Riyasat
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  2. Mehnaz Haneef
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  3. Subuhi Khan
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Correspondence to Mumtaz Riyasat.

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Additional information

Communicated by Rahul Roy.

This work has been done under Senior Research Fellowship (File No. 09/112(0646)/2019-EMR-I dated:13/10/2021) awarded to the second author by Council of Scientific and Industrial Research, Human resource Development Group, New Delhi.

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Riyasat, M., Haneef, M. & Khan, S. Some properties of degenerate Sheffer sequences based on algebraic approach. Indian J Pure Appl Math (2023). https://doi.org/10.1007/s13226-023-00490-3

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