A new generalization of Apostol type Hermite–Genocchi polynomials and its applications

Abstract

By using the modified Milne-Thomson’s polynomial given in Araci et al. (Appl Math Inf Sci 8(6):2803–2808, 2014), we introduce a new concept of the Apostol Hermite–Genocchi polynomials. We also perform a further investigation for aforementioned polynomial and derive some implicit summation formulae and general symmetric identities arising from different analytical means and generating functions method. The results obtained here are an extension of Hermite–Bernoulli polynomials (Pathan and Khan in Mediterr J Math 12:679–695, 2015a) and Hermite–Euler polynomials (Pathan and Khan in Mediterr J Math 2015b, doi:10.1007/s00009-015-0551-1) to Apostol type Hermite–Genocchi polynomials defined in this paper.