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A Note on Type 2 Degenerate q -Euler Polynomials

Author

Listed:
  • 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)

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.

Suggested Citation

  • Taekyun Kim & Dae San Kim & Han Young Kim & Sung-Soo Pyo, 2019. "A Note on Type 2 Degenerate q -Euler Polynomials," Mathematics, MDPI, vol. 7(8), pages 1-11, July.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:681-:d:253109
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