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Multivariate \(p\)-adic fermionic \(q\)-integral on \(\mathbb Z_{p}\) and related multiple zeta-type functions. (English) Zbl 1195.11156

Summary: In [Abstr. Appl. Anal. 2008, Article ID 498173, 7 p. (2008; Zbl 1195.11029)], L.-C. Jang and C.-S. Ryoo constructed generating functions of the multiple twisted Carlitz’s type \(q\)-Bernoulli polynomials and obtained the distribution relation for them. They also raised the following problem: “are there analytic multiple twisted Carlitz’s type \(q\)-zeta functions which interpolate multiple twisted Carlitz’s type \(q\)-Euler (Bernoulli) polynomials?” The aim of this paper is to give a partial answer to this problem. Furthermore we derive some interesting identities related to twisted \(q\)-extension of Euler polynomials and multiple twisted Carlitz’s type \(q\)-Euler polynomials.

MSC:

11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
11B65 Binomial coefficients; factorials; \(q\)-identities
11B68 Bernoulli and Euler numbers and polynomials
33D15 Basic hypergeometric functions in one variable, \({}_r\phi_s\)

Citations:

Zbl 1195.11029
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Full Text: DOI

References:

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