본문 바로가기
KERD
논문KCI 등재

A NOTE ON DEGENERATE BERNOULLI POLYNOMIALS ARISING FROM UMBRAL CALCULUS

1

조회

0

다운로드

0

인용

0

참고문헌

키워드

주제분류수학

초록

In [?, ?], Kim-Kim-Kim defined the λ-analogue of Stirling number of the first and the second kind. In this paper, we find the relationships between various special functions by expressing degenerate Bernoulli polynomials as linear combinations of some special polynomials by using umbral calculus.

Abstract

In [?, ?], Kim-Kim-Kim defined the λ-analogue of Stirling number of the first and the second kind. In this paper, we find the relationships between various special functions by expressing degenerate Bernoulli polynomials as linear combinations of some special polynomials by using umbral calculus.

참고문헌 (39)

  1. L. Ait-Amrange, "Generalized hyper-Lucas numbers and applications", Indian J. Pure Appl. Math, 53(1), pp.62~75 (2022)
  2. H. Alzer, "Identities involving Bernoulli and Euler polynomials", Integral Transforms Spec. Funct, 29(1), pp.43~61 (2018)
  3. T. Arakawa, "Bernoulli numbers and zeta functions" (2014), Springer
  4. M. SELÇUK AYDIN, "A NEW CONSTRUCTION ON THE DEGENERATE HURWITZ-ZETA FUNCTION ASSOCIATED WITH CERTAIN APPLICATIONS", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 25(2), pp.197~206 (2022), 장전수학회
  5. A. Bayad, "Polylogarithms and poly-Bernoulli polynomials", Kyushu J. Math, 65(1), pp.15~24 (2019)
  6. L. Carlitz, "Degenerate Stirling, Bernoulli and Eulerian numbers", Util. Math, 15, pp.51~88 (1979)
  7. K. Chakraborry, "Generalized hypergeometric Bernoulli numbers", Rev. R. Acad. Cienc. Exactas F´ıs. Nat. Ser. A Mat. RACSAM, 115(3), pp.14~ (2021)
  8. 조영기, "On a (r,s)-Analogue of Changhee and Daehee Numbers and Polynomials", Kyungpook Mathematical Journal, 55(2), pp.225~232 (2015), 경북대학교 자연과학대학 수학과
  9. J. Choi, "A note on some identities of Frobeniu-Euler numbers and polynomials", Int. J. Math. Math. Sci., pp.9~ (2012)
  10. L. Comtet, "Advanced combinatorics: The art of finite and infinite expansions" (1974), D. Reidel Publishing Co
  11. R. Dere, "Applications of umbral algebra to some special polynomials", Advanced Studies in Contemporary Mathematics, 22(3), pp.433~438 (2012), 장전수학회[DOI]
  12. W. A. Khan, "Construction of partially degenerate Laguerre–Bernoulli polynomials of the first kind", Appl. Math. Sci. Eng., 30(1), pp.362~375 (2022)
  13. 김택연, "A note on degenerate stirling polynomials of the second kind", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 20(3), pp.319~332 (2017), 장전수학회[DOI]
  14. H. K. Kim, "Degenerate Lah-Bell polynomials arising from degenerate Sheffer sequences", Adv. Differ. Equ., pp.16~ (2020)
  15. 김대산, "Some identities of Bernoulli and Euler polynomials arising form umbral calculus", Advanced Studies in Contemporary Mathematics, 23(1), pp.157~169 (2013), 장전수학회
  16. T. Kim, "An identity of symmetry for the degenerate Frobenius-Euler polynomials", Math. Slovaca, 68(1), pp.239~243 (2018)
  17. 김대산, "Lah-Bell numbers and polynomials", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 23(4), pp.577~586 (2020), 장전수학회
  18. T. Kim, "Some identities on λ-analogue of r-Stirling numbers of the first kind", Filomat, 34(2), pp.451~460 (2020)
  19. T. Kim, "Degenerate polyexponential functions and degenerate Bell polynomials", J. Math. Anal. Appl., 487(2), pp.124017~ (2020)
  20. D. S. Kim, "Degenerate Sheffer sequences and λ-Sheffer sequences", J. Math. Anal. Appl, 493, pp.124521~ (2021)
  21. T. Kim, "Degenerate r-Whitney numbers and degenerate r-DDowling polynomials via boson operators", Adv. in Appl. Math, 140 (2022)
  22. D. S. Kim, "A note on degenerate Bernoulli numbers and polynomials associated with p-adic invariant integral on Zp", Appl. Math. Comput., 259, pp.198~204 (2015)
  23. T. Kim, "Degenerate binomial and Poisson random variables associated with degenerate Lah-Bell polynomials", Open Math, 19(1), pp.1588~1597 (2021)
  24. T. Kim, "Bernoulli polynomials of the second kind and their identities arising from umbral calculus", J. Nonlinear Sci. Appl., 9(3), pp.860~869 (2015)
  25. 김대산, "A NOTE ON DEGENERATE STIRLING NUMBERS OF THE FIRST KIND", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 21(3), pp.393~404 (2018), 장전수학회[DOI]
  26. D. S. Kim, "Some identities on λ-analogue of r-Stirling numbers of the second kind", arXiv:2205.14805, ~
  27. 김대산, "Higher-order Daehee polynomials of the first kind with umbral calculus", Advanced Studies in Contemporary Mathematics, 24(1), pp.5~18 (2014), 장전수학회
  28. T. Kim, "Umbral calculus associated with Frobenius-type Eulerian polynomials", Russ. J. Math. Phys., 21(4), pp.484~493 (2014)
  29. T. Komatsu, "Convolutions of generalized Stirling numbers and degenerate Bernoulli polynomials", Fibonacci Quart, 58, pp.361~366 (2020)
  30. G. Y. Lee, "The linear algebra of the k-Fibonacci matrix", Linear Alg. Appl., 373, pp.75~87 (2003)
  31. D. Lim, "Degenerate, partially degenerate and totally degenerate Daehee numbers and polynomials", Adv. Difference Equ., 2015, pp.14~ (2015)
  32. K. S. Nisar, "Umbral calculus" (2012), LAP LAMBERT Academic Publishing
  33. J. Quaintance, "Combinatorial identities for Stirling numbers" (2016), World Scientific Publishing Co. Pte. Ltd.
  34. 임석훈, "THE n-TH TWISTED CHANGHEE POLYNOMIALS AND NUMBERS", 대한수학회보, 52(3), pp.741~749 (2015), 대한수학회
  35. S. Roman, "The umbral calculus" (2005), Dover Publ. Inc
  36. G. C. Rota, "The classical umbral calculus", SIAM J. Math. Anal., 25(2), pp.694~711 (1994)
  37. C. S. Ryoo, "Differential equations associated with the generalized Euler polynomials of the second kind", J. Comput. Anal. Appl., 24(4), pp.711~716 (2018)
  38. S. Tauber, "Lah Numbers for Fibonacci and Lucas Polynomials", Fibonacci Quart, 6(5), pp.93~99 (1968)
  39. U. Duran, "Construction of the type 2 poly-Frobenius-Genocchi polynomials with their certain applications", Adv. Difference Equ, pp.14~ (2020)

관련 논문AI추천

이 간행물의 다른 논문 (9건)