A Note on a New Type of Degenerate Bernoulli Numbers

By Taekyun Kim, Dae San Kim. 2020

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Studying degenerate versions of various special polynomials has became an active area of research and has yielded many interesting arithmetic and combinatorial results. Here we introduce a degenerate version of the polylogarithm function, the so-called degenerate polylogarithm function. Then we construct a new type of degenerate Bernoulli polynomial and number, the so-called degenerate poly-Bernoulli polynomial and number, by using the degenerate polylogarithm function, and derive several properties concerning the degenerate poly-Bernoulli numbers.

Subfields: Algebra and Number Theory

View Paper: https://www.semanticscholar.org/paper/e181d1e459f59f19e618f7284a962e55b5995c5c