A unified family of multivariable Legendre poly-Genocchi polynomials

T. Usman, N. U. Khan, M. Aman, Y. Gasimov

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 Bn(k)(a,b), poly-Bernoulli polynomials Bn(k)(x,a,b) of Jolany et al., Hermite-Bernoulli polynomials HBn(x,y) of Dattoli et al., HBn(α)(x,y) of Pathan et al. and HGn(k)(x,y) of Khan are generalized to the one SGn(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. 

Tbilisi Mathematical Journal, Vol. 14(2) (2021), pp. 153-170