Some Generalized Properties of Poly-Daehee Numbers and Polynomials Based on Apostol–Genocchi Polynomials

Talha Usman, Nabiullah Khan, Mohd Aman, Shrideh Al-Omari, Kamsing Nonlaopon and Junesang Choi
Additional contact information
Talha Usman: Department of General Requirements, University of Technology and Applied Sciences-Sur, Sur 411, Oman
Nabiullah Khan: Department of Applied Mathematics, Faculty of Engineering and Technology, Aligarh Muslim University, Aligarh 202002, India
Mohd Aman: Department of Applied Mathematics, Faculty of Engineering and Technology, Aligarh Muslim University, Aligarh 202002, India
Shrideh Al-Omari: Department of Scientific Basic Sciences, Faculty of Engineering Technology, Al-Balqa Applied University, Amman 11134, Jordan
Kamsing Nonlaopon: Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
Junesang Choi: Department of Mathematics, Dongguk University, Gyeongju 38066, Korea

Mathematics, 2022, vol. 10, issue 14, 1-15

Abstract: Numerous polynomial variations and their extensions have been explored extensively and found applications in a variety of research fields. The purpose of this research is to establish a unified class of Apostol–Genocchi polynomials based on poly-Daehee polynomials and to explore some of their features and identities. We investigate these polynomials via generating functions and deduce various identities, summation formulae, differential and integral formulas, implicit summation formulae, and several characterized generating functions for new numbers and polynomials. Finally, by using an operational version of Apostol–Genocchi polynomials, we derive some results in terms of new special polynomials. Due to the generic nature of the findings described here, they are used to reduce and generate certain known or novel formulae and identities for relatively simple polynomials and numbers.

Keywords: Bernoulli polynomials; Daehee polynomials; poly-Daehee polynomials; Apostol polynomials; differential operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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