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On a multidimensional Volkenborn integral and higher order Bernoulli numbers

Published online by Cambridge University Press:  17 April 2009

Min-Soo Kim  and
Jin-Woo Son
Min-Soo Kim
Affiliation:
Department of Mathematics, Kyungnam University, Masan 631–701, South Korea e-mail: mskim@mail.kyungnam.ac.kr
Jin-Woo Son
Affiliation:
Department of Mathematics, Kyungnam University, Masan 631–701, South Korea e-mail: sonjin@hanma.kyungnam.ac.kr
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Abstract

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In this paper, using a multidimensional Volkenborn integral, we give a p-adic expression of the higher order Bernoulli numbers. This shows immediately the relation to the sums of products of the ordinary Bernoulli numbers of Dilcher in 1996. We also consider the Mahler expansion of several p-adic variables function, and give some examples.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 65 , Issue 1 , February 2002 , pp. 59 - 71
Copyright
Copyright © Australian Mathematical Society 2002

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