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Non linear recurrences for Apostol-Bernoulli-Euler numbers of higher order

J. Chikhi|A. Bayad
장전수학회 (Jangjeon Mathematical Society)|2012.01|Advanced Studies in Contemporary Mathematics|제22권 제1호|pp. 1-6

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참고문헌

키워드

Bernoulli and Euler numbers and polynomialsEuler’s identities
주제분류수학

초록

We give non linear relations for sums of products of Apostol-Bernoulli and Apostol-Euler numbers of higher order. Our results are extensions of the Bayad-Kim [1] on Apostol-Bernoulli and Apostol-Euler of order 1 and results in [2, 5, 4, 9, 11, 13, 14] on Bernoulli and Euler numbers.

Abstract

We give non linear relations for sums of products of Apostol-Bernoulli and Apostol-Euler numbers of higher order. Our results are extensions of the Bayad-Kim [1] on Apostol-Bernoulli and Apostol-Euler of order 1 and results in [2, 5, 4, 9, 11, 13, 14] on Bernoulli and Euler numbers.

참고문헌 (14)

  1. A. Bayad, "Higher recurrences for Apostol-Bernoulli-Euler numbers"
  2. J. Choi, "Explicit formulas for Bernoulli polynomials of order n", Indian J. Pure Appl. Math, 27, pp.667~674 (1996)
  3. L. Comtet, "Advanced Combinatorics" (1974), Reidel
  4. K. Dilcher, "Sums of products of Bernoulli numbers", J. Number Theory, 60, pp.23~41 (1996)
  5. B. Davis, A, "Sitaramachandrarao, Some identities involving the Riemann zeta function II", Indian J. Pure Appl. Math, 17, pp.1175~1186 (1986)
  6. M. Eie, "A note on Bernoulli numbers and Shintani generalized Bernoulli polynomials", Trans. Amer. Math. soc, 348, pp.1117~1136 (1996)
  7. K. Kamano, "Sums of products of hypergeometric Bernoulli numbers", J. Number Theory, 130, pp.2259~2271 (2010)
  8. T. Kim, "Sums of products of q-Bernoulli numbers", Arch. Math. (Basel), 76, pp.190~195 (1999)
  9. M-S. Kim, "A note on sums of product of Bernoulli numbers", Appl. Math. Lett (2010)[DOI]
  10. T. Kim, "Sums of products of generalized Bernoulli numbers", Int. Math. J., pp.1~7 (2004)
  11. A. Sankaranarayanan, "An identity involving Riemann zeta function", Indian J. Pure Appl.Math, 18, pp.794~800 (1987)
  12. J. Satoh, "Sums of products of two q-Bernoulli numbers", J. Number Theory, 74, pp.173~180 (1999)
  13. A. Petojevic, "Computation of Euler’s type sums of the products of Bernoulli numbers", Appl. Mathematics Letters, 22, pp.796~801 (2009)
  14. W.P. Zhang, "On the several identities of Riemann zeta-function", chines. Sci. Bull, 22, pp.1852~1856 (1991)

관련 논문AI추천

Some closed formulas for generalizations of Bernoulli and Euler numbers and polynomialsH. Yang, Z. Zhang장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2008 · 제11권 제2호A RECURRENCE FORMULA FOR q-EULER NUMBERS OF HIGHER ORDER김영희, 김태균, 최종성장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2010 · 제13권 제3호THEOREMS ON APOSTOL-EULER POLYNOMIALS OF HIGHER ORDER ARISING FROM EULER BASISErdogan Sen장전수학회 · Advanced Studies in Contemporary Mathematics2013 · 제23권 제2호A note on Eulerian polynomials associated with Bernoulli and Euler numbers and polynomials김대산, 김영희, D. V. Dolgy, T. Kim장전수학회 · Advanced Studies in Contemporary Mathematics2012 · 제22권 제3호Some identities of the type 2 degenerate Bernoulli and Euler numbers권종겸, 김대산, 장관우, 정세교장전수학회 · Advanced Studies in Contemporary Mathematics2019 · 제29권 제4호q-analogues of some results for the Apostol-Euler polynomialsQiu-Ming Luo장전수학회 · Advanced Studies in Contemporary Mathematics2010 · 제20권 제1호

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