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

Serkan Araci; Waseem A Khan; Mehmet Acikgoz; Cenap Özel; Poom Kumam

doi:10.1186/s40064-016-2357-4

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

Springerplus. 2016 Jun 24;5(1):860. doi: 10.1186/s40064-016-2357-4. eCollection 2016.

Authors

Serkan Araci¹, Waseem A Khan², Mehmet Acikgoz³, Cenap Özel⁴, Poom Kumam⁵

Affiliations

¹ Department of Economics, Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu University, 27410 Gaziantep, Turkey.
² Department of Mathematics, Integral University, Lucknow, 226026 India.
³ Department of Mathematics, Faculty of Arts and Science, University of Gaziantep, 27310 Gaziantep, Turkey.
⁴ Department of Mathematics, Dokuz Eylül University, 35160 Buca\Izmir, Turkey ; Department of Mathematics, Faculty of Sciences, University of King Abdulaziz, Jeddah, Saudi Arabia.
⁵ Theoretical and Computational Science Center (TaCS) and Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140 Thailand ; Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402 Taiwan.

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.

Keywords: Apostol-Genocchi polynomials; Genocchi polynomials; Hermite polynomials; Hermite–Genocchi polynomials; Summation formulae; Symmetric identities.