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June 2021 A unified family of multivariable Legendre poly-Genocchi polynomials
T. Usman, R. N. U. Khan, M. Aman, Y. Gasimov
Tbilisi Math. J. 14(2): 153-170 (June 2021). DOI: 10.32513/tmj/19322008130

Abstract

In this paper, we introduce a new class of Legendre poly-Genocchi polynomials and give some identities of these polynomials related to the Stirling numbers of the second kind. The concept of poly-Bernoulli numbers $B_{n}^{(k)}(a,b)$, poly-Bernoulli polynomials $B_{n}^{(k)}(x,a,b)$ of Jolany et al., Hermite-Bernoulli polynomials ${}_{H}B_{n}(x,y)$ of Dattoli et al., ${}_{H}B_{n}^{(\alpha)}(x,y)$ of Pathan et al. and ${}_{H}G_{n}^{(k)}(x,y)$ of Khan are generalized to the one $_{S}G_{n}^{(k)}(x,y,z)$. Some implicit summation formulae and general symmetry identities are derived by using different analytical means and applying generating function. These results extended some known summation and identities of Hermite poly-Genocchi numbers and polynomials.

Citation

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T. Usman. R. N. U. Khan. M. Aman. Y. Gasimov. "A unified family of multivariable Legendre poly-Genocchi polynomials." Tbilisi Math. J. 14 (2) 153 - 170, June 2021. https://doi.org/10.32513/tmj/19322008130

Information

Received: 13 January 2021; Accepted: 2 February 2021; Published: June 2021
First available in Project Euclid: 2 July 2021

Digital Object Identifier: 10.32513/tmj/19322008130

Subjects:
Primary: 33C10
Secondary: 05A10, 05A15, 33C45, 33C90

Rights: Copyright © 2021 Tbilisi Centre for Mathematical Sciences

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Vol.14 • No. 2 • June 2021
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