**Title:** FORMULAS AND COMBINATORIAL SUMS INCLUDING SPECIAL NUMBERS ON *P*-ADIC INTEGRALS

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

**Article ID:** MTJPAM-D-19-00006; **Volume 1 / Issue 1 / Year 2019**, Pages 129-139

**Document Type:** Research Paper

**Author(s):** Neslihan Kilar ^{a}

^{a}Department of Mathematics, Faculty of Science University of Akdeniz TR-07058 Antalya-Turkey

Received: 2 October 2019, Accepted: 5 November 2019, Available online: 28 November 2019.

**Corresponding Author:** Neslihan Kilar (Email address: neslihankilar@gmail.com)

**Full Text:** PDF

**Abstract**

The main motivation of this work is to give some formulas for the special numbers, which were recently introduced by Kilar and Simsek with the aid of the *p*-adic integrals methods. These formulas are related to the some well-known families of special numbers and polynomials such as the negative order Bernoulli polynomials, the negative order Euler numbers and polynomials, the Stirling numbers, the array polynomials, the combinatorial numbers including the numbers *y*_{1}(*n*,*k*;*λ*), the numbers *y*_{2}(*n*,*k*;*λ*), the numbers *y*_{3}(*n*,*k*;*λ*;*a*,*b*), the central factorial numbers, and combinatorial sums.

**Keywords:** Bernoulli numbers and polynomials, the Euler numbers and polynomials, the Stirling numbers of the second kind, the array polynomials, the numbers *y*_{1}(*n*,*k*;*λ*), the numbers *y*_{2}(*n*,*k*;*λ*), the numbers *y*_{3}(*n*,*k*;*λ*;*a*,*b*), the central factorial numbers

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