**Title:** A Unified Family of Apostol-Bernoulli Based Poly-Daehee Polynomials

**Montes Taurus J. Pure Appl. Math.** / ISSN: 2687-4814

**Article ID:** MTJPAM-D-20-00009; **Volume 3 / Issue 3 / Year 2021 (Special Issue)**, Pages 1-11

**Document Type:** Research Paper

**Author(s):** Talha Usman ^{a} , Nabiullah Khan ^{b} , Mohd Saif ^{c} , Junesang Choi ^{d}

^{a}Department of Mathematics, School of Basic and Applied Sciences, Lingaya’s Vidyapeeth, Faridabad 121002, Haryana, India

^{b}Department of Applied Mathematics, Faculty of Engineering and Technology, Aligarh Muslim University, Aligarh 202002, India

^{c}Department of Applied Mathematics, Faculty of Engineering and Technology, Aligarh Muslim University, Aligarh 202002, India

^{d}Department of Mathematics, Dongguk University, Gyeongju 38066, Republic of Korea

Received: 22 April 2019, Accepted: 3 June 2020, Published: 25 April 2021.

**Corresponding Author:** Junesang Choi (Email address: junesang@dongguk.ac.kr)

**Full Text:** PDF

**Abstract**

We introduce a unified family of Apostol-Bernoulli based poly-Daehee polynomials. Then we provide a number of formulas involving these unified polynomials such as differential formulas, addition formulas, summation formulas, and an implicit summation formula. The identities presented here, being general, are pointed out to yield the corresponding formulas associated with relatively simple polynomials. Further we provide several other polynomials similar to these unified polynomials.

**Keywords:** Apostol-Bernoulli based poly-Daehee polynomials and numbers, Apostol-Euler based poly-Daehee polynomials and numbers, Apostol-Genocchi based poly-Daehee polynomials and numbers, Differential formula, Addition formula, Summation formula, Implicit summation formula

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