A note on partially degenerate Hermite-Bernoulli polynomials of the first kind

Volume 30, Issue 3, pp 255--271 https://doi.org/10.22436/jmcs.030.03.05
Publication Date: January 12, 2023 Submission Date: June 11, 2022 Revision Date: August 02, 2022 Accteptance Date: August 31, 2022

Authors

W. A. Khan - Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, P.O Box 1664, Al Khobar 31952, Saudi Arabia. M. S. Alatawi - Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia.


Abstract

In this paper, we introduce a new class of partially degenerate Hermite-Bernoulli polynomials of the first kind and generalized Gould-Hopper-partially degenerate Bernoulli polynomials of the first kind and present some properties and identities of these polynomials. A new class of polynomials generalizing different classes of Hermite polynomials such as the real Gould-Hopper, as well as the 1-d and 2-d holomorphic, ternary and polyanalytic complex Hermite polynomials and their relationship to the partially degenerate Hermite-Bernoulli polynomials of the first kind are also discussed.


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ISRP Style

W. A. Khan, M. S. Alatawi, A note on partially degenerate Hermite-Bernoulli polynomials of the first kind, Journal of Mathematics and Computer Science, 30 (2023), no. 3, 255--271

AMA Style

Khan W. A., Alatawi M. S., A note on partially degenerate Hermite-Bernoulli polynomials of the first kind. J Math Comput SCI-JM. (2023); 30(3):255--271

Chicago/Turabian Style

Khan, W. A., Alatawi, M. S.. " A note on partially degenerate Hermite-Bernoulli polynomials of the first kind." Journal of Mathematics and Computer Science, 30, no. 3 (2023): 255--271


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