Multivariate $p$-Adic Fermionic $q$-Integral on ${\mathbb{Z}}_{p}$ and Related Multiple Zeta-Type Functions
Min-Soo Kim, Taekyun Kim, and Jin-Woo Son
Source: Abstr. Appl. Anal. Volume 2008 (2008), 13 pages.
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 $p$-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.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aaa/1220969175
Digital Object Identifier: doi:10.1155/2008/304539
Zentralblatt MATH identifier:
05313193
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.
Mathematical Reviews (MathSciNet):
MR2280996
Zentralblatt MATH:
1112.11012
Digital Object Identifier: doi:10.1016/j.jmaa.2006.03.037
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.
Mathematical Reviews (MathSciNet):
MR2370678
Zentralblatt MATH:
1160.11013
Digital Object Identifier: doi:10.1016/j.jmaa.2007.07.027
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.
Mathematical Reviews (MathSciNet):
MR2470850
Digital Object Identifier: doi:10.1134/S1061920808040055
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.
Mathematical Reviews (MathSciNet):
MR2356180
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.
Mathematical Reviews (MathSciNet):
MR2393118
Digital Object Identifier: doi:10.1155/2008/390857
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.
Mathematical Reviews (MathSciNet):
MR2379516
Digital Object Identifier: doi:10.1155/2008/816129
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.
Mathematical Reviews (MathSciNet):
MR2122609
Zentralblatt MATH:
1114.11019
Digital Object Identifier: doi:10.1016/j.jnt.2004.07.003
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.
Mathematical Reviews (MathSciNet):
MR2393476
Zentralblatt MATH:
1140.11311
Digital Object Identifier: doi:10.1155/2008/738603
Y. Yamasaki, ``On $q$-analogues of the Barnes multiple zeta functions,'' Tokyo Journal of Mathematics, vol. 29, no. 2, pp. 413--427, 2006.
Mathematical Reviews (MathSciNet):
MR2284981
Digital Object Identifier: doi:10.3836/tjm/1170348176
Project Euclid: euclid.tjm/1170348176
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.
Mathematical Reviews (MathSciNet):
MR2264580
Zentralblatt MATH:
1110.11029
Digital Object Identifier: doi:10.1007/s00605-005-0369-1
Abstract and Applied Analysis
