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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