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arXiv · 1201.3701

A probabilistic interpretation of the Volkenborn integral

A. Bhandari·C. Vignat
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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.

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A. Bhandari, C. Vignat. 2012-01-18. A probabilistic interpretation of the Volkenborn integral. https://arxiv.org/abs/1201.3701

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