A Note on Polyexponential and Unipoly Functions
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- 1 January 2019
- journal article
- research article
- Published by Pleiades Publishing Ltd in Russian Journal of Mathematical Physics
- Vol. 26 (1), 40-49
- https://doi.org/10.1134/s1061920819010047
Abstract
In this paper, we introduce polyexponential functions as an inverse to the polylogarithm functions, construct type 2 poly-Bernoulli polynomials by using this and derive various properties of type 2 poly-Bernoulli numbers. Then we introduce unipoly functions attached to each suitable arithmetic function as a universal concept which includes the polylogarithm and polyexponential functions as special cases. By making use of unipoly functions, we define unipoly-Bernoulli polynomials, type 2 unipoly-Bernoulli numbers, and unipoly-Bernoulli numbers of the second kind, and show some basic properties for them.Keywords
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