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SOME SYMMETRIC IDENTITIES OF THE MODIFIED q-EULER POLYNOMIALS UNDER SYMMETRIC GROUP OF DEGREE FOUR

김태균|J. J. Seo
장전수학회 (Jangjeon Mathematical Society)|2015.04|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제18권 제2호|pp. 211-216|DOI 10.17777/pjms.2015.18.2.008

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참고문헌

키워드

modified q-Euler polynomials under S4
주제분류수학

초록

Recently, several authors have studied q-Euler polynomials which are given by En,q(x) = ∫ Zp [x + y]nq dμ-q(y), (n ≥ 0). In this paper, we ∫ study the modi ed q-Euler polynomials which are de ned by n,q(x) = Zp [x+y]nq dμ-1(y), (n ≥ 0). The purpose of this paper is to give identities of symmetry for the modi ed q-Euler polynomials under S4.

Abstract

Recently, several authors have studied q-Euler polynomials which are given by En,q(x) = ∫ Zp [x + y]nq dμ-q(y), (n ≥ 0). In this paper, we ∫ study the modi ed q-Euler polynomials which are de ned by n,q(x) = Zp [x+y]nq dμ-1(y), (n ≥ 0). The purpose of this paper is to give identities of symmetry for the modi ed q-Euler polynomials under S4.

참고문헌 (11)

  1. L. Carlitz, "q-Bernoulli and Eulerian numbers", Trans. Amer. math. Soc., 76(2), pp.332~350 (1954)
  2. T. Kim, "Identities of symmetry for higher-order -Euler polynomials", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 17(2), pp.161~167 (2014), 장전수학회
  3. 김태균, "A NOTE ON SYMMETRIC IDENTITIES FOR THE GENERALIZED q-EULER POLYNOMIALS OF THE SECOND KIND", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 17(3), pp.375~381 (2014), 장전수학회
  4. T. Kim, "Symmetric identities for q-Euler polynomials under the fourth Dihedral group", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 18(2), pp.217~223 (2015), 장전수학회
  5. D. S. Kim, "Symmetry identities of higher-order q-Euler polynomials under the symmetric group of degree four", ~
  6. D. S. Kim, "Identities of symmetry for generalized q-Euler polynomials arising from multivariate fermionic -adic integral on Z_p", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 17(4), pp.519~525 (2014), 장전수학회
  7. T. Kim, "q-Euler numbers ans polynomials associated with p-adic q-integrals", J. Nonliner Math. Phys, 14(1), pp.15~27 (2007)
  8. T. Kim, "Symmetry of power sum polynomials and multivariate fermionic p-adic invariant integral on Zp", Russ. J. Math. Phys., 16(1), pp.93~96 (2009)
  9. 김태균, "A STUDY ON THE q-EULER NUMBERS AND THE FERMIONIC q-INTEGRAL OF THE PRODUCT OF SEVERAL TYPE q-BERNSTEIN POLYNOMIALS ON Zp", Advanced Studies in Contemporary Mathematics, 23(1), pp.1~4 (2013), 장전수학회
  10. Q. -M. Luo, "Relationships between generalized Bernoulli numbers and polynomials and generalized Euler numbers and polynomials", Adv. Stud. Contemp. Math., 7(1), pp.11~18 (2003)
  11. Erdogan Sen, "THEOREMS ON APOSTOL-EULER POLYNOMIALS OF HIGHER ORDER ARISING FROM EULER BASIS", Advanced Studies in Contemporary Mathematics, 23(2), pp.337~346 (2013), 장전수학회

관련 논문AI추천

IDENTITIES OF SYMMETRY FOR MODIFIED CARLITZ'S q-BERNOULLI POLYNOMIALS UNDER SYMMETRIC GROUP OF DEGREE 4H. I. Kwon, J. J. Seo, T. Kim장전수학회 · Advanced Studies in Contemporary Mathematics2015 · 제25권 제2호SOME NEW IDENTITIES OF SYMMETRY FOR THE MODIFIED GENERALIZED q-EULER POLYNOMIALS UNDER S5J.-J. SEO, T. Kim장전수학회 · Advanced Studies in Contemporary Mathematics2015 · 제25권 제3호LINEAR SYMMETRY OF THE MODIFIED q-EULER POLYNOMIALS최상기장전수학회 · Advanced Studies in Contemporary Mathematics2018 · 제28권 제2호SYMMETRIC IDENTITIES OF HIGHER-ORDER CARLITZ'S q-BERNOULLI POLYNOMIALS UNDER SYMMETRIC GROUP OF DEGREE FOURT. Kim장전수학회 · Advanced Studies in Contemporary Mathematics2015 · 제25권 제2호SYMMETRIC IDENTITIES OF TYPE 2 BERNOULLI AND EULER POLYNOMIALS UNDER S3권종겸, 박진우, 윤상조장전수학회 · Advanced Studies in Contemporary Mathematics2020 · 제30권 제3호SYMMETRIC IDENTITIES OF DEGENERATE q-BERNOULLI POLYNOMIALS UNDER SYMMETRY GROUP S3권혁인, 김태균, 서종진, Dmitry V. Dolgy장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2016 · 제19권 제1호

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