본문 바로가기
KERD
논문KCI 등재

Some identities of degenerate Genocchi polynomials

임동규
대한수학회 (The Korean Mathematical Society)|2016.03|대한수학회보 (Bulletin of the KMS)|제53권 제2호|pp. 569-579

0

조회

0

다운로드

3

인용

0

참고문헌

키워드

degenerate Genocchi polynomialfemionic $p$-adic integral
주제분류수학

초록

L. Carlitz introduced higher order degenerate Euler polynomials in \cite{A4,A5} and studied a degenerate Staudt-Clausen theorem in \cite{A4}. D. S. Kim and T. Kim gave some formulas and identities of degenerate Euler polynomials which are derived from the fermionic $p$-adic integrals on $\mathbb{Z}_p$ (\mbox{see~~\cite{A11}}). In this paper, we introduce higher order degenerate Genocchi polynomials. And we give some formulas and identities of degenerate Genocchi polynomials which are derived from the fermionic $p$-adic integrals on $\mathbb{Z}_p$.

Abstract

L. Carlitz introduced higher order degenerate Euler polynomials in \cite{A4,A5} and studied a degenerate Staudt-Clausen theorem in \cite{A4}. D. S. Kim and T. Kim gave some formulas and identities of degenerate Euler polynomials which are derived from the fermionic $p$-adic integrals on $\mathbb{Z}_p$ (\mbox{see~~\cite{A11}}). In this paper, we introduce higher order degenerate Genocchi polynomials. And we give some formulas and identities of degenerate Genocchi polynomials which are derived from the fermionic $p$-adic integrals on $\mathbb{Z}_p$.

참고문헌 (30)

  1. Serkan Araci, "A unified generating function of the q-genocchi polynomials with their interpolation functions", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 15(2), pp.227~233 (2012), 장전수학회[DOI]
  2. Bayad, "IDENTITIES FOR THE BERNOULLI, THE EULER AND THE GENOCCHI NUMBERS AND POLYNOMIALS", Advanced Studies in Contemporary Mathematics, 20(2), pp.247~253 (2010), 장전수학회
  3. I. N.. Cangul, "ON THE HIGHER-ORDER w-q-GENOCCHI NUMBERS", Advanced Studies in Contemporary Mathematics, 19(1), pp.39~57 (2009), 장전수학회
  4. L. Carlitz, "A degenerate Staudt-Clausen theorem", Arch. Math. (Basel), 7, pp.28~33 (1956)
  5. L. Carlitz, "Degenerate Stirling, Bernoulli and Eulerian numbers", Utilitas Math, 15, pp.51~88 (1979)
  6. S. Gaboury, "Some explicit formulas for certain new classes of Bernoulli, Euler and Genocchi polynomials", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 17(1), pp.115~123 (2014), 장전수학회
  7. D. Kang, "Some identities of higher order Genocchi polynomials arising from higher order Genocchi basis", J. Comput. Anal. Appl, 17(1), pp.141~146 (2014)
  8. D. S. Kim, "A note on Boole polynomials", Integral Transforms Spec. Funct, 25(8), pp.627~633 (2014)
  9. D. S. Kim, "Some identities of degenerate Euler polynomials arising from p-adic fermionic integrals on Zp", Integral Transforms Spec. Funct, 26(4), pp.295~302 (2015)
  10. D. S. Kim, "Higher-order Degenerate Euler Polynomials", Applied Mathematical Sciences, 9(2), pp.57~73 (2015)
  11. 김대산, "Barnes-type degenerate Bernoulli polynomials", Advanced Studies in Contemporary Mathematics, 25(1), pp.121~146 (2015), 장전수학회
  12. D. S. Kim, "A note on the lambda-Daehee polynomials", Int. J. Math. Anal. (Ruse), 7(61-64), pp.3069~3080 (2013)
  13. T. Kim, "A note on q-Volkenborn integration", Proc. Jangjeon Math. Soc, 8(1), pp.13~17 (2005)
  14. T. Kim, "A note on the q-Genocchi numbers and polynomials", J. Inequal. Appl, 2007, pp.8~ (2007)
  15. T. Kim, "On the q-extension of Euler and Genocchi numbers", J. Math. Anal. Appl, 326(2), pp.1458~1465 (2007)
  16. T. Kim, "q-Euler numbers and polynomials associated with p-adic q-integrals", J. Nonlinear Math. Phys, 14(1), pp.15~27 (2007)
  17. T. Kim, "Note on q-Genocchi numbers and polynomials", Advanced Studies in Contemporary Mathematics, 17(1), pp.9~15 (2008), 장전수학회
  18. T. Kim, "On the multiple q-Genocchi and Euler numbers", Russ. J. Math. Phys, 15(4), pp.481~486 (2008)
  19. 김태균, "New approach to q-Euler, Genocchi numbers and their interpolation functions", Advanced Studies in Contemporary Mathematics, 18(2), pp.105~112 (2009), 장전수학회
  20. T. Kim, "Symmetry of power sum polynomials and multivariate fermionic p-adic invari-ant integral on Zp", Russ. J. Math. Phys, 16(1), pp.93~96 (2009)
  21. 김태균, "SOME IDENTITIES FOR THE BERNOULLI, THE EULER AND THE GENOCCHI NUMBERS AND POLYNOMIALS", Advanced Studies in Contemporary Mathematics, 20(1), pp.23~28 (2010), 장전수학회
  22. T. Kim, "A note on the identities of special polynomials", Ars Combin, 113A, pp.97~106 (2014)
  23. T. Kim, "Some properties on the p-adic invariant integral on Zp associated with Genocchi and Bernoulli polynomials", J. Comput. Anal. Appl, 13(7), pp.1201~1207 (2011)
  24. T. Kim, "Some identities of Genocchi polynomials arising from Genocchi basis", J. Inequal. Appl, 2013, pp.43~ (2013)
  25. Y.-H. Kim, "Interpolation functions of the q-Genocchi and the q-Euler polynomials of higher order", J. Comput. Anal. Appl, 12(1-B), pp.228~238 (2010)
  26. Kurt, "THE MULTIPLICATION FORMULAE FOR THE GENOCCHI POLYNOMIALS", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 13(1), pp.89~96 (2010), 장전수학회
  27. H. Ozden, "p-adic distribution of the unification of the Bernoulli, Euler and Genocchi polynomials", Appl. Math. Comput, 218(3), pp.970~973 (2011)
  28. 임석훈, "ON THE q-GENOCCHI NUMBERS AND POLYNOMIALS ASSOCIATED WITH q-ZETA FUNCTION", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 12(3), pp.261~267 (2009), 장전수학회
  29. C. S. Ryoo, "On the generalized q-Genocchi numbers and polynomials of higher-order", Adv. Difference Equ, 2011, pp.8~ (2011)
  30. H. M. Srivastava, "Some families of Genocchi type polynomials and their interpolation functions", Integral Transforms Spec. Funct, 23(12), pp.919~938 (2012)

관련 논문AI추천

SOME IDENTITIES FOR DEGENERATE EULER NUMBERS AND POLYNOMIALS ARISING FROM DEGENERATE BELL POLYNOMIALS권혁인, 김태균, 서종진, Dmitry V. Dolgy장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2016 · 제19권 제3호Modified degenerate Euler polynomials권혁인, 김태균, 서종진장전수학회 · Advanced Studies in Contemporary Mathematics2016 · 제26권 제1호On degenerate $q$-Bernoulli polynomials김태균대한수학회 · 대한수학회보2016 · 제53권 제4호SOME IDENTITIES OF CARLITZ'S TYPE DEGENERATE q-CHANGHEE POLYNOMIALS AND NUMBERS박진우, Jongkyum Kwon, Yunjae Kim장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2021 · 제24권 제1호A note on degenerate Bell numbers and polynomials associated with p-adic integral on Zp권혁인, 김태균, 서종진, DMITY V. DOLGY장전수학회 · Advanced Studies in Contemporary Mathematics2016 · 제26권 제3호Some identities on the Bernstein and q-Genocchi polynomials김현미대한수학회 · 대한수학회보2013 · 제50권 제4호

이 간행물의 다른 논문 (24건)

Inequalities for the angular derivatives of certain classes of holomorphic functions in the unit discB\"{u}lent Nafi \"{O}rnekpp. 325-334Existence results for anti-periodic boundary value problems of nonlinear second-order impulsive $q_k$-difference equationsJessada Tariboon, Sotiris K. Ntouyas, Phollakrit Thiramanuspp. 335-350Entropy-based goodness of fit test for a composite hypothesisSangyeolLeepp. 351-363A note on the value distribution of $f^2(f')^n$ for $n\geq 2$Yan Jiangpp. 365-371On difference quotients of Chebyshev polynomialsJung Hee Lee, 김선홍pp. 373-386
원문 보기