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On the modified degenerate Bernoulli polynomials

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In this paper, we consider the modi ed degenerate Bernoulli polynomials and numbers which are different from Carlitz's degenerate Bernoulli polynomials and numbers. Finally, we give some identities and formulas of these polynomials and numbers.

Abstract

In this paper, we consider the modi ed degenerate Bernoulli polynomials and numbers which are different from Carlitz's degenerate Bernoulli polynomials and numbers. Finally, we give some identities and formulas of these polynomials and numbers.

참고문헌 (9)

  1. 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
  2. L. Carlitz, "Degenerate Stirling, Bernoulli and Eulerian numbers", Utilitas Math, 15, pp.51~88 (1979)
  3. 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
  4. 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
  5. 김대산, "Barnes' multiple Bernoulli and Hermite mixed-type polynomials", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 18(1), pp.7~19 (2015), 장전수학회
  6. 김대산, "Some arithmetic properties of Bernoulli and Euler numbers", Advanced Studies in Contemporary Mathematics, 22(4), pp.467~480 (2012), 장전수학회
  7. 김태균, "On the weighted q-Bernoulli numbers and polynomials", Advanced Studies in Contemporary Mathematics, 21(2), pp.207~215 (2011), 장전수학회
  8. T. Kim, "Some properties on the integral of the product of several Euler polynomials", Quaest. Math, 38(4), pp.553~562 (2015)
  9. C. S. Ryoo, "A new identities on the q-Bernoulli numbers and polynomials", Advanced Studies in Contemporary Mathematics, 21(2), pp.161~169 (2011), 장전수학회

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