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Expansions of generalized Carlitz -Bernoulli polynomials

이상훈|김태균|김대산|서종진
장전수학회 (Jangjeon Mathematical Society)|2014.04|Advanced Studies in Contemporary Mathematics|제24권 제2호|pp. 167-173

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참고문헌

키워드

Generalized Carlitz's q-Bernoulli polynomialMultivariate q-Volkenborn integral
주제분류수학

초록

In this paper, we consider the expansion of the generalized Carlitz q-Bernulli polynomials and give the identities of symmetry for those polynomials.

Abstract

In this paper, we consider the expansion of the generalized Carlitz q-Bernulli polynomials and give the identities of symmetry for those polynomials.

참고문헌 (22)

  1. A. Bayad, "Non linear recurrences for Apostol-Bernoulli-Euler numbers of higher order", Advanced Studies in Contemporary Mathematics, 22(1), pp.1~6 (2012), 장전수학회
  2. L. Carlitz, "Expansions of q-Bernoulli numbers", Duke Math. J, 25, pp.355~364 (1958)
  3. 최종성, "A note on the extended q-Bernoulli numbers and polynomials", Advanced Studies in Contemporary Mathematics, 21(4), pp.351~354 (2011), 장전수학회
  4. Dan Ding, "Some identities related to the Apostol-Euler and Apostol-Bernoulli polynomials", Advanced Studies in Contemporary Mathematics, 20(1), pp.7~21 (2010), 장전수학회
  5. Yuan He, "Symmetric identities for Carlitz's q-Bernoulli numbers and polynomials", Adv. Dif-ference Equ, 2013, pp.246~ (2013)
  6. L.-C. Jang, "Some new identities on the twisted Car-litz's q-Bernoulli numbers and q-Bernstein polynomials", J. Inequal. Appl, 2011, pp.52~ (2011)
  7. "MR 2837907 (2012m:33014)", ~
  8. D. Kim, "A note on Carlitz q-Bernoulli numbers and polynomials", Adv. Dif-ference Equ, 2012(44), pp.10~ (2012)
  9. 김대산, "Identities associated with generalized twisted Euler polynomials twisted by ramified roots of unity", Advanced Studies in Contemporary Mathematics, 22(3), pp.363~377 (2012), 장전수학회
  10. 김대산, "Abundant symmetry for higher-order Bernoulli polynomials (I)", Advanced Studies in Contemporary Mathematics, 23(3), pp.459~479 (2013), 장전수학회
  11. T. Kim, "On explicit formulas of p-adic q-L-functions", MR 1269069(95c : 11140), 48(1), pp.73~86 (1994)
  12. T. Kim, "q-Volkenborn integration", Russ. J. Math. Phys, 9(3), pp.288~299 (2002)
  13. T. Kim, "q-Bernoulli numbers and polynomials associated with Gaussian binomial coefficients", Russ. J. Math. Phys, 15(1,), pp.51~57 (2008)
  14. T. Kim, "q-Bernstein polynomials associated with q-Stirling num-bers and Carlitz's q-Bernoulli numbers", Abstr. Appl. Anal (2010)
  15. T. Kim, "A note on Carlitz's q-Bernoulli measure", J. Comput. Anal. Appl, 13(3), pp.590~595 (2011)
  16. T. Kim, "Generalized Carlitz's q-Bernoulli numbers in the p-adic number eld", Adv. Stud. Contemp. Math. (Pusan), 2, pp.9~19 (2000)
  17. T. Kim, "A note on p-adic Carlitz's q-Bernoulli numbers", Bull. Austral. Math. Soc, 62(2), pp.227~234 (2000)
  18. 김영희, "Symmetry of power sum and twisted Bernoulli polynomials", Advanced Studies in Contemporary Mathematics, 18(2), pp.127~133 (2009), 장전수학회
  19. H. Ozden, "Remarks on q-Bernoulli numbers associated with Daehee numbers", Advanced Studies in Contemporary Mathematics, 18(1), pp.41~48 (2009), 장전수학회
  20. J.-W. Park, "A note on the modi ed Carlitz's q-Bernoulli numbers and polynomials", J. Comput. Anal. Appl, 15(4,), pp.647~654 (2013)
  21. S.-H. Rim, "Some identities on the extended Carlitz's q-Bernoulli numbers and polynomials", J. Comput. Anal. Appl, 14(3), pp.536~543 (2012)
  22. Yilmaz Simsek, "Generating functions of the twisted Bernoulli numbers and polynomials associated with their interpolation functions", Advanced Studies in Contemporary Mathematics, 16(2), pp.251~278 (2008), 장전수학회

관련 논문AI추천

IDENTITIES OF SYMMETRY FOR DEGENERATE q-BERNOULLI POLYNOMIALSH-I Kwon, J. J. Seo, T. Kim장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2015 · 제18권 제4호A note on the modified q-Bernoulli polynomials권종겸, 박진우, 서종진, 임석훈장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2013 · 제16권 제4호A note on the extended q-Bernoulli numbers and polynomials김영희, 김태균, 최종성장전수학회 · Advanced Studies in Contemporary Mathematics2011 · 제21권 제4호A note on symmetric identities of the generalized Carlitz's type q-Euler polynomials of the first kind김태균, 서종진, 장유선, Dmitry V. Dolgy장전수학회 · Advanced Studies in Contemporary Mathematics2014 · 제24권 제3호On degenerate $q$-Bernoulli polynomials김태균대한수학회 · 대한수학회보2016 · 제53권 제4호A note on Carlitz's type q-Changhee numbers and polynomials권혁인, 김태균, 장관우, Dmitry V. Dolgy장전수학회 · Advanced Studies in Contemporary Mathematics2017 · 제27권 제4호

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