q-Volkenborn integration. II

T. Kim, L. C. Jang, D. W. Park and C. Adiga
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 9, 2003, Number 4, Pages 83–89
Full paper (PDF, 169 Kb)

Details

Authors and affiliations

T. Kim
Institute of Science Education,
Kongju National University, Kongju 314-701, S. Korea

L. C. Jang
Department of Math. and Comput. Sci.,
KonKuk University, Chungju , Korea

D. W. Park
Department of Mathematics Education, Kongju
National University, Kongju 314-701, Korea

C. Adiga
Department of Studies in Math., Universuty
of Mysore, Mysore-570 006, India

Abstract

By using q-Volkenborn integration, the multiple Changhee q-Bernoulli numbers which are an interesting analogue of Barnes’ multiple Bernoulli numbers were constructed in [4]. The object of this paper is to define the extension of multiple Changhee q-Bernoulli numbers and to give the new explicit formulas which are related to these numbers.

Keywords

• p-adic q-integrals
• Multiple Barnes’ Bernoulli numbers

AMS Classification

• 11S80
• 11B68
• 11M99

References

1. E. W. Barnes, On the theory of the multiple gamma functions, Trans. Camb. Philos. Soc. 19 (1904), 374-425.
2. H.S.Cho, E.S.Kim, Translation-invariant p-adic integration on , Proc. Jangjeon Math. 3 (2001), 45-52.
3. T. Kim, Sums of products of q-Bernoulli numbers, Arch. Math. 76 (2001), 190-195.
4. T. Kim, Non-Arichimedean q-integrals associated with multiple Changhee q-Bernoulli polynomials, Russ. J. Math. Phys. 10(1) (2003), 91-98.
5. T. Kim, q-Volkenborn integration, Russ. J. Math. Phys. 9 (2002), 288-299.
6. T. Kim, q-Riemann zeta functions, to appear in Inter. J. Math. Math. Sci. (2004), 00-00.
7. T. Kim, An invariant p-adic integral associated with Daehee numbers, Integral Trans. Special Funct. 13 (2002), 65-69.
8. Y.H. Kim, D.W. Park, L.C.Jang, A note on q-analogue of Volkenborn integral, Adv. Stud. Contemp. Math. 4 (2002), 159-163.