## 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, $${}_r\phi_s$$

Zbl 1195.11029
Full Text:

### References:

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