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A note on degenerate Apostol-Bernoulli numbers and polynomials

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In this paper, we consider the degenerate Apostol-Bernoulli numbers and polynomials due to L. Carlitz. and we investigate some properties for these numbers and polynomials

Abstract

In this paper, we consider the degenerate Apostol-Bernoulli numbers and polynomials due to L. Carlitz. and we investigate some properties for these numbers and polynomials

참고문헌 (11)

  1. A. Bayad, "Apostol–Euler polynomials and asymptotics for negative binomial reciprocals", Advanced Studies in Contemporary Mathematics, 24(1), pp.33~37 (2014), 장전수학회
  2. A. Bayad, "Identities for Apostol-type Frobenius-Euler polynomials resulting from the study of a nonlinear operator", Russ. J. Math. Phys, 23(2), pp.164~171 (2016)
  3. A. Bayad, "Higher recurrences for Apostol-Bernoulli-Euler numbers", Russ. J. Math. Phys, 19(1), pp.1~10 (2012)
  4. L. Carlitz, "Degenerate Stirling, Bernoulli and Eulerian numbers", Utilitas Math, 15, pp.51~88 (1979)
  5. L. Carlitz, "A degenerate Staudt-Clausen theorem", Arch. Math. (Basel), 7, pp.28~33 (1956)
  6. 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
  7. Y. He, "General convolution identities for Apostol-Bernoulli Euler and Genocchi polynomials", J. Nonlinear Sci. Appl, 9(6), pp.4780~4797 (2016)
  8. K.-W. Hwang, "Interpolation functions of q-extensions of Apostol's type Euler polynomials", J. Inequal. Appl, pp.12~ (2009)
  9. T. Kim, "Apostol-Euler polynomials arising from umbral calculus", Adv. Difference Equ, 301, pp.7~ (2013)
  10. Qiu-Ming Luo, "q-analogues of some results for the Apostol-Euler polynomials", Advanced Studies in Contemporary Mathematics, 20(1), pp.103~113 (2010), 장전수학회
  11. S. Roman, "The Umbral Calculus, Pure and Applied Mathematics, 111", pp.193~ (1984), Academic Press. Inc

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