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    Araci, Serkan Acikgoz, Mehmet and Ağyüz, Erkan 2014. On the Dirichlet’s type of Eulerian polynomials. Mathematical Sciences, Vol. 8, Issue. 2,


    2012. Zeta and q-Zeta Functions and Associated Series and Integrals.


    Choi, Junesang Anderson, P.J. and Srivastava, H.M. 2009. Carlitz’s q-Bernoulli and q-Euler numbers and polynomials and a class of generalized q-Hurwitz zeta functions. Applied Mathematics and Computation, Vol. 215, Issue. 3, p. 1185.


    Choi, Junesang Anderson, P.J. and Srivastava, H.M. 2008. Some q-extensions of the Apostol–Bernoulli and the Apostol–Euler polynomials of order n, and the multiple Hurwitz zeta function. Applied Mathematics and Computation, Vol. 199, Issue. 2, p. 723.


    Ryoo, C.S. and Kim, Taekyun 2008. A numerical computation of the structure of the roots of q-Bernoulli polynomials. Journal of Computational and Applied Mathematics, Vol. 214, Issue. 2, p. 319.


    Ryoo, C. S. 2007. A numerical investigation of the structure of the roots ofq-Bernoulli polynomials. Journal of Applied Mathematics and Computing, Vol. 23, Issue. 1-2, p. 205.


    Kim, Min-Soo and Son, Jin-Woo 2003. Bernoulli numbers in p-adic analysis. Applied Mathematics and Computation, Vol. 146, Issue. 1, p. 289.


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  • Bulletin of the Australian Mathematical Society, Volume 62, Issue 2
  • October 2000, pp. 227-234

A note on p-adic Carlitz's q-Bernoulli numbers

  • Taekyun Kim (a1) and Seog-Hoon Rim (a2)
  • DOI: http://dx.doi.org/10.1017/S0004972700018700
  • Published online: 01 April 2009
Abstract

In a recent paper I have shown that Carlitz's q-Bernoulli number can be represented as an integral by the q-analogue μq of the ordinary p-adic invariant measure. In the p-adic case, J. Satoh could not determine the generating function of q-Bernoulli numbers. In this paper, we give the generating function of q-Bernoulli numbers in the p-adic case.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]T. Kim , ‘On a q-analogue of the p-adic log gamma functions and related integrals’, J. Number Theory 76 (1999), 320329.

[2]J. Satoh , ‘q-Analogue of Riemann's ζ-function and q-Euler numbers’, J. Number Theory 31 (1989), 346362.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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