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A note on type 2 degenerate Euler and Bernoulli polynomials

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Recently, several authors have studied degenerate Bernoulli and Euler polynomials in connection with many special numbers and poly- nomials. In this paper, we study the type 2 degenerate Bernoulli and Euler polynomials and give some properties for these polynomials. In particu- lar, these polynomials are closely related to central factorial numbers of the second kind. In addition, we give some identities of these polynomials associated with the central factorial numbers of the second kind.

Abstract

Recently, several authors have studied degenerate Bernoulli and Euler polynomials in connection with many special numbers and poly- nomials. In this paper, we study the type 2 degenerate Bernoulli and Euler polynomials and give some properties for these polynomials. In particu- lar, these polynomials are closely related to central factorial numbers of the second kind. In addition, we give some identities of these polynomials associated with the central factorial numbers of the second kind.

참고문헌 (15)

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  5. 장관우, "Degenerate Changhee numbers and polynomials of the second kind", Advanced Studies in Contemporary Mathematics, 27(4), pp.609~624 (2017), 장전수학회[DOI]
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  7. T. Kim, "Degenerate central factorial numbers of the second kind (communi-cated)", ~
  8. 김태균, "A NOTE ON CENTRAL FACTORIAL NUMBERS", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 21(4), pp.575~588 (2018), 장전수학회[DOI]
  9. 김태균, "A NOTE ON CATALAN NUMBERS ASSOCIATED WITH p-ADIC INTEGRAL ON Zp", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 19(3), pp.493~501 (2016), 장전수학회
  10. M. Merca, "Connections between central factorial numbers and Bernoulli polynomials. Pe-riod", Math. Hungar, 73(2), pp.259~264 (2016)
  11. I. Mezo, "some identities of the r-Whitney numbers", Aequationes Math, 90(2), pp.393~406 (2016)
  12. S. Nadarajah, "Factorial, raw and central moments", Math. Sci, 41(1), pp.65~71 (2016)
  13. Sung-Soo Pyo, "Degenerate Daehee Numbers of the Third Kind", Mathematics, 6(11), pp.239~ (2018), MDPI AG[DOI]
  14. R. Riordan, "Combinatorial identities", pp.13~ (1968), John Wiley & Sons, Inc
  15. S. Roman, "The umbral calculus. Pure and Applied Mathematics, 111", pp.10~ (1984), Academic Press, Inc

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