English

A probabilistic interpretation of the Volkenborn integral

Number Theory 2012-01-19 v1

Abstract

In this paper, we provide a probabilistic interpretation of the Volkenborn integral; this allows us to extend results by T. Kim et al about sums of Euler numbers to sums of Bernoulli numbers. We also obtain a probabilistic representation of the multidimensional Volkenborn integral which allows us to derive a multivariate version of Raabe's multiplication theorem for the higher-order Bernoulli and Euler polynomials.

Keywords

Cite

@article{arxiv.1201.3701,
  title  = {A probabilistic interpretation of the Volkenborn integral},
  author = {A. Bhandari and C. Vignat},
  journal= {arXiv preprint arXiv:1201.3701},
  year   = {2012}
}
R2 v1 2026-06-21T20:06:10.342Z