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A NOTE ON THE TYPE 2 POLY-APOSTOL-BERNOULLI POLYNOMIALS

장이채|권종겸
장전수학회 (Jangjeon Mathematical Society)|2020.04|Advanced Studies in Contemporary Mathematics|제30권 제2호|pp. 253-262

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참고문헌

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polylogarithm functionpoly-Bernoulli polynomialstype 2 poly- Bernoulli polynomialsApstol Bernoulli polynomialstype 2 poly-Apostol-Bernoulli polynomials
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초록

Recently, Kim-Kim ([6]) have studied the type2 poly-Bernoulli poly- nomials by using the polylogarithm functions. In this paper, we de ne the type 2 poly-Apostol-Bernoulli polynomials and investigate some properties for them. Furthermore, by making use of unipoly function, we de ne the type 2 unipoly- Apostol-Bernoulli numbers and show some basic properties for them.

Abstract

Recently, Kim-Kim ([6]) have studied the type2 poly-Bernoulli poly- nomials by using the polylogarithm functions. In this paper, we de ne the type 2 poly-Apostol-Bernoulli polynomials and investigate some properties for them. Furthermore, by making use of unipoly function, we de ne the type 2 unipoly- Apostol-Bernoulli numbers and show some basic properties for them.

참고문헌 (16)

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  2. 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
  3. M. A. Boutiche, "Some remarks on the generalized Apostol-Bernoulli and Apostol-Euler polynomials", Indian J. Pure Appl. Math., 50(4), pp.1133~1145 (2019)
  4. Y. He, "Some new identities for the Apostol-Bernoulli polynomials and the Apostol-Genocchi polynomials", Appl. Math. Comput., 262, pp.31~41 (2015)
  5. 김대산, "A note on degenerate Eulerian numbers and polynomials", Advanced Studies in Contemporary Mathematics, 27(4), pp.431~440 (2017), 장전수학회[DOI]
  6. D. S. Kim, "A note on polyexponential and unipoly functions", Russ. J. Math. Phys., 26(1), pp.40~49 (2019)
  7. T. Kim, "Degenerate Laplace transform and degenerate gamma function", Russ. J. Math. Phys., 24(2), pp.241~248 (2017)
  8. T. Kim, "Degenerate Laplace transform and degenerate gamma function", Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Mat. RACSAM, 113(3), pp.2783~2791 (2019)
  9. T. Kim, "On type 2 degenerate Bernoulli and Euler polyno-mials of complex variable", Adv. Difference Equ., 490, pp.15~ (2019)
  10. T. Kim, "A note on central Bell numbers and polynomials", Russ. J.Math.Phys., 27(1), pp.76~81 (2020)
  11. 김태균, "A NOTE ON DEGENERATE GAMMA FUNCTION AND DEGENERATE STIRLING NUMBER OF THE SECOND KIND", Advanced Studies in Contemporary Mathematics, 28(2), pp.207~214 (2018), 장전수학회[DOI]
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  14. 김태균, "On the analogs of Bernoulli and Euler numbers, related identities and zeta and L-functions", 대한수학회지, 45(2), pp.435~453 (2008), 대한수학회
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  16. IREM KUCUKOGLU, "REMARKS ON RECURRENCE FORMULAS FOR THE APOSTOL-TYPE NUMBERS AND POLYNOMIALS", Advanced Studies in Contemporary Mathematics, 28(4), pp.643~658 (2018), 장전수학회[DOI]

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