A Note on Polyexponential and Unipoly Functions

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 funct...

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Bibliographic Details
Published inRussian journal of mathematical physics Vol. 26; no. 1; pp. 40 - 49
Main Authors Kim, D. S., Kim, T.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.01.2019
Springer Nature B.V
Subjects
Functions (mathematics)
Mathematical analysis
Mathematical and Computational Physics
Mathematical functions
Physics
Physics and Astronomy
Polynomials
Theoretical
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1061-9208
1555-6638
DOI:10.1134/S1061920819010047