Abstract and Applied Analysis

A New q -Analogue of Bernoulli Polynomials Associated with p -Adic q -Integrals

Lee-Chae Jang

Full-text: Open access

Abstract

We will study a new q -analogue of Bernoulli polynomials associated with p -adic q -integrals. Furthermore, we examine the Hurwitz-type q -zeta functions, replacing p -adic rational integers x with a q -analogue [ x ] q for a p -adic number q with | q 1 | p < 1 , which interpolate q -analogue of Bernoulli polynomials.

Article information

Source
Abstr. Appl. Anal., Volume 2008 (2008), Article ID 295307, 6 pages.

Dates
First available in Project Euclid: 10 February 2009

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1234298992

Digital Object Identifier
doi:10.1155/2008/295307

Mathematical Reviews number (MathSciNet)
MR2448391

Zentralblatt MATH identifier
1217.11116

Citation

Jang, Lee-Chae. A New $q$ -Analogue of Bernoulli Polynomials Associated with $p$ -Adic $q$ -Integrals. Abstr. Appl. Anal. 2008 (2008), Article ID 295307, 6 pages. doi:10.1155/2008/295307. https://projecteuclid.org/euclid.aaa/1234298992


Export citation

References

  • L. Carlitz, ``$q$-Bernoulli numbers and polynomials,'' Duke Mathematical Journal, vol. 15, no. 4, pp. 987--1000, 1948.
  • M. Cenkci, Y. Simsek, and V. Kurt, ``Further remarks on multiple $p$-adic $q$-$L$-function of two variables,'' Advanced Studies in Contemporary Mathematics (Kyungshang), vol. 14, no. 1, pp. 49--68, 2007.
  • T. Kim, ``On explicit formulas of $p$-adic $q$-$L$-functions,'' Kyushu Journal of Mathematics, vol. 48, no. 1, pp. 73--86, 1994.
  • T. Kim, ``$q$-Volkenborn integration,'' Russian Journal of Mathematical Physics, vol. 9, no. 3, pp. 288--299, 2002.
  • T. Kim, ``On a $q$-analogue of the $p$-adic log gamma functions and related integrals,'' Journal of Number Theory, vol. 76, no. 2, pp. 320--329, 1999.
  • T. Kim, L. C. Jang, and S. H. Rim, ``An extension of $q$-zeta function,'' International Journal of Mathematics and Mathematical Sciences, vol. 2004, no. 49, pp. 2649--2651, 2004.
  • T. Kim, ``The modified $q$-Euler numbers and polynomials and polynomials,'' Advanced Studies in Contemporary Mathematics, vol. 16, pp. 161--170, 2008.
  • H. Ozden, Y. Simsek, S.-H. Rim, and I. N. Cangul, ``A note on $p$-adic $q$-Euler measure,'' Advanced Studies in Contemporary Mathematics (Kyungshang), vol. 14, no. 2, pp. 233--239, 2007.
  • T. Kim, ``On $p$-adic $q$-$L$-functions and sums of powers,'' Discrete Mathematics, vol. 252, no. 1--3, pp. 179--187, 2002.
  • T. Kim, ``An invariant $p$-adic $q$-integrals on $\mathbbZ_p$,'' Applied Mathematics Letters, vol. 21, no. 2, pp. 105--108, 2008.
  • T. Kim, L. C. Jang, S.-H. Rim, and H.-K. Pak, ``On the twisted $q$-zeta functions and $q$-Bernoulli polynomials,'' Far East Journal of Applied Mathematics, vol. 13, no. 1, pp. 13--21, 2003.
  • K. Shriatani and S. Yamamoto, ``On a $p$-adic interpolation function for the Euler numbers and its derivatives,'' Memoirs of the Faculty of Science, Kyushu University, vol. 76, no. 2, pp. 320--329, 1999.
  • Y. Simsek, ``On $p$-adic twisted $q$-$L$-functions related to generalized twisted Bernoulli numbers,'' Russian Journal of Mathematical Physics, vol. 13, no. 3, pp. 340--348, 2006. \endthebibliography