New integral formulas and identities involving special numbers and functions derived from certain class of special combinatorial sums


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ŞİMŞEK Y.

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, vol.115, no.2, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 115 Issue: 2
  • Publication Date: 2021
  • Doi Number: 10.1007/s13398-021-01006-6
  • Journal Name: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, MathSciNet, zbMATH, DIALNET, Civil Engineering Abstracts
  • Keywords: Generating function, Special numbers and polynomials, Bernoulli-type numbers and polynomials, Fibonacci numbers, Harmonic numbers, Stirling numbers, Daehee numbers, Digamma function, Hurwitz zeta function
  • Akdeniz University Affiliated: Yes

Abstract

By applying p-adic integral, in Simsek (Montes Taurus J Pure Appl Math 3(1):38-61, 2021), we constructed generating function for the special numbers and polynomials involving novel combinatorial sums and numbers. The aim of this paper is to use these combinatorial sums and numbers to derive various new formulas and relations associated with the Bernstein basis functions, the Fibonacci numbers, the Harmonic numbers, the alternating Harmonic numbers, the Bernoulli polynomials of higher order, binomial coefficients and new integral formulas for the Riemann integral. We also investigate and study on open problems involving these numbers. Moreover, we give relation among these numbers, the Digamma function, and the Euler constant. Moreover, by applying special values of these combinatorial sums, we give decomposition of the multiple Hurwitz zeta function which interpolates the Bernoulli polynomials of higher order. Finally, we give conclusions for the results of this paper with some comments and observations.