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

Abstract

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
• Special numbers and polynomials
• Generating functions