Abstract and Applied Analysis

Multivariate p -Adic Fermionic q -Integral on p and Related Multiple Zeta-Type Functions

Min-Soo Kim, Taekyun Kim, and Jin-Woo Son

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Abstract

In 2008, Jang et al. 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.

Article information

Source
Abstr. Appl. Anal., Volume 2008 (2008), Article ID 304539, 13 pages.

Dates
First available in Project Euclid: 9 September 2008

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1220969175

Digital Object Identifier
doi:10.1155/2008/304539

Mathematical Reviews number (MathSciNet)
MR2411042

Zentralblatt MATH identifier
1195.11156

Citation

Kim, Min-Soo; Kim, Taekyun; Son, Jin-Woo. Multivariate $p$ -Adic Fermionic $q$ -Integral on ${\mathbb{Z}}_{p}$ and Related Multiple Zeta-Type Functions. Abstr. Appl. Anal. 2008 (2008), Article ID 304539, 13 pages. doi:10.1155/2008/304539. https://projecteuclid.org/euclid.aaa/1220969175


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References

  • T. Kim, ``On the $q$-extension of Euler and Genocchi numbers,'' Journal of Mathematical Analysis and Applications, vol. 326, no. 2, pp. 1458--1465, 2007.
  • T. Kim, ``On $p$-adic interpolating function for $q$-Euler numbers and its derivatives,'' Journal of Mathematical Analysis and Applications, vol. 339, no. 1, pp. 598--608, 2008.
  • T. Kim, ``On the čommentComment on ref. [7?]: Please update the information of this reference, if possible. multiple $q$-Genocchi and Euler numbers,'' to appear in Russian Journal of Mathematical Physics.
  • T. Kim, M.-S. Kim, L.-C. Jang, and S.-H. Rim, ``New $q$-Euler numbers and polynomials associated with $p$-adic $q$-integrals,'' Advanced Studies in Contemporary Mathematics, vol. 15, no. 2, pp. 243--252, 2007.
  • H. Ozden, I. N. Cangul, and Y. Simsek, ``Multivariate interpolation functions of higher-order $q$-Euler numbers and thier applications,'' Abstract and Applied Analysis, vol. 2008, Article ID 390857, 16 pages, 2008.
  • H. Ozden and Y. Simsek, ``Interpolation čommentComment on ref. [12?]: Please update the information of this reference, if possible. function of the $(h,q)$-extension of twisted Euler numbers,'' Computers & Mathematics with Applications. In press.
  • H. Ozden, I. N. Cangul, and Y. Simsek, ``Remarks on sum of products of $(h,q)$-twisted Euler polynomials and numbers,'' Journal of Inequalities and Applications, vol. 2008, Article ID 816129, 8 pages, 2008.
  • T. Kim, L.-C. Jang, and C.-S. Ryoo, ``Note on $q$-extensions of Euler numbers and polynomials of higher order,'' Journal of Inequalities and Applications, vol. 2008, Article ID 371295, 9 pages, 2008.
  • Y. Simsek, ``$q$-analogue of twisted $l$-series and $q$-twisted Euler numbers,'' Journal of Number Theory, vol. 110, no. 2, pp. 267--278, 2005.
  • L.-C. Jang and C.-S. Ryoo, ``A note on the multiple twisted Carlitz's type $q$-Bernoulli polynomials,'' Abstract and Applied Analysis, vol. 2008, Article ID 498173, 7 pages, 2008.
  • L.-C. Jang, ``Multiple twisted $q$-Euler numbers and polynomials associated with $p$-adic $q$-integrals,'' Advances in Difference Equations, vol. 2008, Article ID 738603, 11 pages, 2008.
  • Y. Yamasaki, ``On $q$-analogues of the Barnes multiple zeta functions,'' Tokyo Journal of Mathematics, vol. 29, no. 2, pp. 413--427, 2006.
  • M. Wakayama and Y. Yamasaki, ``Integral representations of $q$-analogues of the Hurwitz zeta function,'' Monatshefte für Mathematik, vol. 149, no. 2, pp. 141--154, 2006.