Abstract
In this paper, we consider higher order Barnes-type q-Bernoulli polynomials and numbers and investigate some identities of them. Furthermore, we discuss some identities of higher order Barnes-type q-Euler polynomials and numbers.
Highlights
Let p be a given odd prime number
Higher order Bernoulli polynomials are defined by Kim to be t et
Higher order Barnestype Bernoulli polynomials are defined by Kim to be r t eait
Summary
Let p be a given odd prime number. Throughout this paper, we assume that Zp, Qp andCp will, respectively, denote the rings of p-adic integers, the fields of p-adic numbers and the completion of algebraic closure of Q p. Higher order Bernoulli polynomials are defined by Kim to be t et – Higher order Barnestype Bernoulli polynomials are defined by Kim to be r t eait – Ar) is called higher order Barnes-type Bernoulli numbers.
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