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Russian Journal of Mathematical Physics

, Volume 26, Issue 1, pp 40–49 | Cite as

A Note on Polyexponential and Unipoly Functions

  • D. S. KimEmail author
  • T. KimEmail author
Article
  • 13 Downloads

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.

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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Department of MathematicsSogang UniversitySeoulRepublic of Korea
  2. 2.Department of MathematicsKwangwoon UniversitySeoulRepublic of Korea

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