Barnes-type multiple q-zeta functions and q-Euler polynomials

The purpose of this paper is to present a systemic study of some families of multiple q-Euler numbers and polynomials and we construct multiple q-zeta functions which interpolate multiple q-Euler numbers at a negative integer. This is a partial answer to the open question in a previous publication (see Kim et al 2001 J. Phys. A: Math. Gen. 34 7633–8).

[1]  Andrei Khrennikov,et al.  Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models , 2011 .

[2]  Taekyun Kim,et al.  Some identities on the q-Euler polynomials of higher order and q-stirling numbers by the fermionic p-adic integral on ℤp , 2009 .

[3]  Taekyun Kim Note on the Euler q-zeta functions , 2009 .

[4]  Taekyun Kim q-Extension of the Euler formula and trigonometric functions , 2007 .

[5]  S. Rim,et al.  A note on p-adic q-Euler measure , 2007, math/0702868.

[6]  T. Kim The Modified q-Euler numbers and polynomials , 2007, math/0702523.

[7]  Y. Simsek,et al.  $q$-Bernoulli Numbers and Polynomials Associated with Multiple $q$-Zeta Functions and Basic $L$-series , 2005, math/0502019.

[8]  Taekyun Kim,et al.  On multivariate p-adic q-integrals , 2001 .

[9]  Hans J. H. Tuenter,et al.  A Symmetry of Power Sum Polynomials and Bernoulli Numbers , 2001, Am. Math. Mon..

[10]  Simon Ruijsenaars,et al.  On Barnes' Multiple Zeta and Gamma Functions , 2000 .

[11]  Andrew Khrennikov,et al.  Statistical interpretation of p‐adic quantum theories with p‐adic valued wave functions , 1995 .

[12]  Andrei Khrennikov,et al.  p-Adic Valued Distributions in Mathematical Physics , 1994 .

[13]  Elias Deeba,et al.  Stirling's series and Bernoulli numbers , 1991 .

[14]  Katsumi Shiratani,et al.  On a p-adic interpolation function for the Euler numbers and its derivatives , 1985 .

[15]  Yilmaz Simsek,et al.  Remarks on q-Bernoulli numbers associated with Daehee numbers , 2009 .

[16]  Yilmaz Simsek,et al.  ON THE HIGHER-ORDER w-q-GENOCCHI NUMBERS , 2009 .

[17]  Jang Lee Chae,et al.  A study on the distribution of twisted q-Genocchi polynomials , 2009 .

[18]  Taekyun Kim,et al.  The modified q-Euler numbers and polynomials , 2008 .

[19]  S. Albeverio,et al.  On the Markovian Behavior of p-Adic Random Dynamical Systems , 2001 .

[20]  V. S. Vladimirov,et al.  P-adic analysis and mathematical physics , 1994 .

[21]  Siegfried Bosch,et al.  p-adic Analysis , 1990 .