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Open AccessFeature PaperArticle

Type 2 Degenerate Poly-Euler Polynomials

1
School of Electronic and Electric Engineering, Daegu University, Gyeongsan 38453, Korea
2
Department of Mathematics Education, Daegu Catholic University, Gyeongsan 38430, Korea
3
Graduate School of Education, Konkuk University, Seoul 143-701, Korea
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(6), 1011; https://doi.org/10.3390/sym12061011
Received: 20 May 2020 / Revised: 9 June 2020 / Accepted: 11 June 2020 / Published: 15 June 2020
In recent years, many mathematicians have studied the degenerate versions of many special polynomials and numbers. The polyexponential functions were introduced by Hardy and rediscovered by Kim, as inverses to the polylogarithms functions. The paper is divided two parts. First, we introduce a new type of the type 2 poly-Euler polynomials and numbers constructed from the modified polyexponential function, the so-called type 2 poly-Euler polynomials and numbers. We show various expressions and identities for these polynomials and numbers. Some of them involving the (poly) Euler polynomials and another special numbers and polynomials such as (poly) Bernoulli polynomials, the Stirling numbers of the first kind, the Stirling numbers of the second kind, etc. In final section, we introduce a new type of the type 2 degenerate poly-Euler polynomials and the numbers defined in the previous section. We give explicit expressions and identities involving those polynomials in a similar direction to the previous section. View Full-Text
Keywords: poly-Euler polynomials and numbers; degenerate poly-Euler polynomials and numbers; modified degenerate polyexponential functions; poly-Bernoulli polynomials; the Stirling numbers poly-Euler polynomials and numbers; degenerate poly-Euler polynomials and numbers; modified degenerate polyexponential functions; poly-Bernoulli polynomials; the Stirling numbers
MDPI and ACS Style

Lee, D.S.; Kim, H.K.; Jang, L.-C. Type 2 Degenerate Poly-Euler Polynomials. Symmetry 2020, 12, 1011.

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