AN ALGEBRAIC APPROACH TO DEGENERATE APPELL POLYNOMIALS AND THEIR HYBRID FORMS VIA DETERMINANTS*

doi:10.1007/s10473-023-0215-3

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (2): 719-735.doi: 10.1007/s10473-023-0215-3

AN ALGEBRAIC APPROACH TO DEGENERATE APPELL POLYNOMIALS AND THEIR HYBRID FORMS VIA DETERMINANTS^*

Mumtaz Riyasat^1,†, Tabinda Nahid², Subuhi Khan²

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

收稿日期:2021-12-29 修回日期:2022-03-31 出版日期:2023-03-25 发布日期:2023-04-12
通讯作者: †Mumtaz Riyasat, E-mail: mumtazrst@gmail.com
作者简介:Tabinda Nahid, E-mail: tabindanahid@gmail.com; Subuhi Khan, E-mail: subuhi2006@gmail.com

AN ALGEBRAIC APPROACH TO DEGENERATE APPELL POLYNOMIALS AND THEIR HYBRID FORMS VIA DETERMINANTS^*

Mumtaz Riyasat^1,†, Tabinda Nahid², Subuhi Khan²

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

Received:2021-12-29 Revised:2022-03-31 Online:2023-03-25 Published:2023-04-12
Contact: †Mumtaz Riyasat, E-mail: mumtazrst@gmail.com
About author:Tabinda Nahid, E-mail: tabindanahid@gmail.com; Subuhi Khan, E-mail: subuhi2006@gmail.com

摘要/Abstract

摘要： 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.

关键词: degenerate Bernoulli polynomials, degenerate Appell polynomials, determinant expressions, degenerate hybrid Appell polynomials

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.

Key words: degenerate Bernoulli polynomials, degenerate Appell polynomials, determinant expressions, degenerate hybrid Appell polynomials

Mumtaz Riyasat, Tabinda Nahid, Subuhi Khan. AN ALGEBRAIC APPROACH TO DEGENERATE APPELL POLYNOMIALS AND THEIR HYBRID FORMS VIA DETERMINANTS^*[J]. 数学物理学报(英文版), 2023, 43(2): 719-735.

Mumtaz Riyasat, Tabinda Nahid, Subuhi Khan. AN ALGEBRAIC APPROACH TO DEGENERATE APPELL POLYNOMIALS AND THEIR HYBRID FORMS VIA DETERMINANTS^*[J]. Acta mathematica scientia,Series B, 2023, 43(2): 719-735.

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AN ALGEBRAIC APPROACH TO DEGENERATE APPELL POLYNOMIALS AND THEIR HYBRID FORMS VIA DETERMINANTS^*

AN ALGEBRAIC APPROACH TO DEGENERATE APPELL POLYNOMIALS AND THEIR HYBRID FORMS VIA DETERMINANTS^*

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