A Note on Type 2 Degenerate q -Euler Polynomials

Taekyun Kim, Dae San Kim, Han Young Kim and Sung-Soo Pyo
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Taekyun Kim: Department of Mathematics, Kwangwoon University, Seoul 01897, Korea
Dae San Kim: Department of Mathematics, Sogang University, Seoul 04107, Korea
Han Young Kim: Department of Mathematics, Kwangwoon University, Seoul 01897, Korea
Sung-Soo Pyo: Department of Mathematics Education, Silla University, Busan 46958, Korea

Mathematics, 2019, vol. 7, issue 8, 1-11

Abstract: Recently, type 2 degenerate Euler polynomials and type 2 q -Euler polynomials were studied, respectively, as degenerate versions of the type 2 Euler polynomials as well as a q -analog of the type 2 Euler polynomials. In this paper, we consider the type 2 degenerate q -Euler polynomials, which are derived from the fermionic p -adic q -integrals on Z p , and investigate some properties and identities related to these polynomials and numbers. In detail, we give for these polynomials several expressions, generating function, relations with type 2 q -Euler polynomials and the expression corresponding to the representation of alternating integer power sums in terms of Euler polynomials. One novelty about this paper is that the type 2 degenerate q -Euler polynomials arise naturally by means of the fermionic p -adic q -integrals so that it is possible to easily find some identities of symmetry for those polynomials and numbers, as were done previously.

Keywords: type 2 degenerate q -Euler polynomials; fermionic p -adic q -integral (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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