A note on degenerate Euler polynomials arising from umbral calculus

Volume 32, Issue 4, pp 332--347 http://dx.doi.org/10.22436/jmcs.032.04.04

Publication Date: November 03, 2023 Submission Date: June 28, 2023 Revision Date: August 23, 2023 Accteptance Date: September 01, 2023

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Authors

S. S. Lee - Department of Education, Mathematics Education Major, Graduate School of Education, Daegu University, 38453, Republic of Korea. J.-W. Park - Department of Mathematics Education, Daegu University, 38453, Republic of Korea.

Abstract

In this paper, we derive some interesting identities that found relationships between degenerate Euler polynomials and some special polynomials by using umbral calculus and \(\lambda\)-analogue of the Stirling numbers of the first and the second kind, respectively. In addition, we present explicit formulas for representations of the degenerate Euler polynomials.

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Keywords

• Degenerate Euler polynomials
• umbral calculus
• \(\lambda\)-analogue of the Stirling numbers of the first and second kind

MSC

•  33E20
•  05A30
•  11B83
•  11S80

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