Some symmetric identities for the generalized Bernoulli, Euler and Genocchi polynomials associated with Hermite polynomials

Waseem A Khan; Hiba Haroon

doi:10.1186/s40064-016-3585-3

Some symmetric identities for the generalized Bernoulli, Euler and Genocchi polynomials associated with Hermite polynomials

Springerplus. 2016 Nov 4;5(1):1920. doi: 10.1186/s40064-016-3585-3. eCollection 2016.

Authors

Waseem A Khan¹, Hiba Haroon¹

Affiliation

¹ Department of Mathematics, Integral University, Lucknow, 226026 India.

Abstract

In 2008, Liu and Wang established various symmetric identities for Bernoulli, Euler and Genocchi polynomials. In this paper, we extend these identities in a unified and generalized form to families of Hermite-Bernoulli, Euler and Genocchi polynomials. The procedure followed is that of generating functions. Some relevant connections of the general theory developed here with the results obtained earlier by Pathan and Khan are also pointed out.

Keywords: Bernoulli polynomials; Euler polynomials and Genocchi polynomials; Hermite polynomials; Hermite–Bernoulli polynomials; Hermite–Euler polynomials; Hermite–Genocchi polynomials; Symmetric identities.