Identities and recurrence relations of special numbers and polynomials of higher order by analysis of their generating functions

Yilmaz Simsek; Daeyeoul Kim

doi:10.1186/s13660-018-1815-7

Identities and recurrence relations of special numbers and polynomials of higher order by analysis of their generating functions

J Inequal Appl. 2018;2018(1):220. doi: 10.1186/s13660-018-1815-7. Epub 2018 Aug 22.

Authors

Yilmaz Simsek¹, Daeyeoul Kim²

Affiliations

¹ 1Department of Mathematics, Faculty of Science, Akdeniz University, Antalya, Turkey.
² 2Department of Mathematics and Institute of Pure and Applied Mathematics, Chonbuk National University, Jeonju-si, South Korea.

Abstract

The aim of this is to give generating functions for new families of special numbers and polynomials of higher order. By using these generating functions and their functional equations, we derive identities and relations for these numbers and polynomials. Relations between these new families of special numbers and polynomials and Bernoulli numbers and polynomials are given. Finally, recurrence relations and derivative formulas, which are related to these numbers and polynomials, are given.

Keywords: Apostol–Bernoulli numbers and polynomials; Bernoulli numbers and polynomials; Generating functions; Special numbers and polynomials.