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arXiv · 1903.05270

A symbolic approach to the poly-Bernoulli numbers

T. Wakhare·C. Vignat
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Abstract

We present a symbolic representation for the poly-Bernoulli numbers. This allows us to prove several new iterated integral representations for the poly-Bernoulli numbers, including an integral transform of the Bernoulli-Barnes numbers. We also deduce some new recurrences for the poly-Bernoulli numbers. Finally, we use these results to present a new iterated integral representation for the Arakawa-Kaneko zeta function, including a nonlinear integral transform of the Barnes zeta function.

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T. Wakhare, C. Vignat. 2019-03-13. A symbolic approach to the poly-Bernoulli numbers. https://arxiv.org/abs/1903.05270

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