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
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
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