본문 바로가기
KERD
논문KCI 등재

Some properties of the Bernoulli numbers of the second kind and their generating function

Feng Qi|Jiao-Lian Zhao
대한수학회 (The Korean Mathematical Society)|2018.11|대한수학회보 (Bulletin of the KMS)|제55권 제6호|pp. 1909-1920

0

조회

0

다운로드

1

인용

0

참고문헌

키워드

generating functionrecurrence relationexplicit formulasolutiondifferential equationBernoulli number of the second kindStirling number of the first kinddeterminantal expression
주제분류수학

초록

In the paper, the authors find a common solution to three series of differential equations related to the generating function of the Bernoulli numbers of the second kind and present a recurrence relation, an explicit formula in terms of the Stirling numbers of the first kind, and a determinantal expression for the Bernoulli numbers of the second kind.

Abstract

In the paper, the authors find a common solution to three series of differential equations related to the generating function of the Bernoulli numbers of the second kind and present a recurrence relation, an explicit formula in terms of the Stirling numbers of the first kind, and a determinantal expression for the Bernoulli numbers of the second kind.

참고문헌 (36)

  1. N. Bourbaki, "Elements of Mathematics (Berlin)" (2004), Springer-Verlag
  2. N. D. Cahill, "Fibonacci determinants", College Math. J, 3, pp.221~225 (2002)
  3. L. Comtet, "Advanced Combinatorics" (1974), D. Reidel Publishing Co.
  4. B.-N. Guo, "Some identities and an explicit formula for Bernoulli and Stirling numbers", J. Comput. Appl. Math, 255, pp.568~579 (2014)
  5. S. Hu, "Two closed forms for the Apostol-Bernoulli polynomials", Ra-manujan J, 46(1), pp.103~117 (2018)
  6. G. Nemes, "An asymptotic expansion for the Bernoulli numbers of the second kind", J. Integer Seq, 14(4), pp.6~ (2011)
  7. F. Qi, "An integral representation, complete monotonicity, and inequalities of Cauchy numbers of the second kind", J. Number Theory, 144, pp.244~255 (2014)
  8. F. Qi, "Explicit formulas for computing Bernoulli numbers of the second kind and Stirling numbers of the first kind", Filomat, 28(2), pp.319~327 (2014)
  9. F. Qi, "Derivatives of tangent function and tangent numbers", Appl. Math. Comput, 268, pp.844~858 (2015)
  10. F. Qi, "A new formula for the Bernoulli numbers of the second kind in terms of the Stirling numbers of the first kind", Publ. Inst. Math. (Beograd) (N.S.), 100(114), pp.243~249 (2016)
  11. F. Qi, "Diagonal recurrence relations for the Stirling numbers of the first kind", Contrib. Discrete Math, 11(1), pp.22~30 (2016)
  12. F. Qi, "Diagonal recurrence relations, inequalities, and monotonicity related to the Stirling numbers of the second kind", Math. Inequal. Appl, 19(1), pp.313~323 (2016)
  13. On tridiagonal determinants and the Cauchy product of central Delannoy numbers, "F. Qi", ResearchGate, ~ (2016)
  14. F. Qi, "Two closed forms for the Bernoulli polynomials", J. Number Theory, 159, pp.89~100 (2016)
  15. F. Qi, "Explicit formulas for derangement numbers and their generating function", J. Nonlinear Funct. Anal, 2016, pp.10~ (2016)
  16. F. Qi, "Some determinantal expressions and recurrence relations of the Bernoulli polynomials", Mathematics, 4(4), pp.11~ (2016)
  17. F. Qi, "A determinantal expression and a recurrence relation for the Euler polynomials", Adv. Appl. Math. Sci, 16(9), pp.297~309 (2017)
  18. F. Qi, "Explicit and recursive formulas, integral representations, and properties of the large Schroder numbers", Kragujevac J. Math, 41(1), pp.121~141 (2017)
  19. F. Qi, "Explicit formulas and recurrence relations for higher order Eulerian polynomials", Indag. Math. (N.S.), 28(4), pp.884~891 (2017)
  20. F. Qi, "Expressing the generalized Fibonacci polynomials in terms of a tridiagonal determinant", Matematiche (Catania), 72(1), pp.167~175 (2017)
  21. F. Qi, "Two nice determinantal expressions and a recurrence relation for the Apostol-Bernoulli polynomials", J. Indones. Math. Soc, 23(1), pp.81~87 (2017)
  22. F. Qi, "A diagonal recurrence relation for the Stirling numbers of the first kind", Appl. Anal. Discrete Math, 12(1), pp.153~165 (2018)
  23. Feng Qi, "Explicit formulas and identities for the Bell polynomials and a sequence of polynomials applied to differential equations", Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 113(1), pp.1~9 (2019), Springer Nature[DOI]
  24. Feng Qi, "Some properties of the Catalan–Qi function related to the Catalan numbers", SpringerPlus, 5(1), pp.1126~ (2016), Springer Nature[DOI]
  25. Feng Qi, "Some identities for a sequence of unnamed polynomials connected with the Bell polynomials", Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 112 (2018), Springer Nature[DOI]
  26. F. Qi, "Two explicit formulas of the Schroder numbers", Integers, 16, pp.15~ (2016)
  27. F. Qi, "Several formulas for special values of the Bell polynomials of the second kind and applications", J. Appl. Anal. Comput, 7(3), pp.857~871 (2017)
  28. F. Qi, "A recovery of two determinantal representations for derangement numbers", Cogent Math, 3, pp.7~ (2016)
  29. F. Qi, "A representation for derangement numbers in terms of a tridiagonal determinant", Kragujevac J. Math, 42(1), pp.7~14 (2018)
  30. F. Qi, "Notes on a family of inhomogeneous linear ordinary differential equations", Adv. Appl. Math. Sci, 17(4), pp.361~368 (2018)
  31. F. Qi, "Simplifying differential equations concerning degenerate Bernoulli and Euler numbers", Trans. A. Razmadze Math. Inst, 172(1), pp.90~94 (2018)
  32. Feng Qi, "AN INTEGRAL REPRESENTATION, SOME INEQUALITIES, AND COMPLETE MONOTONICITY OF THE BERNOULLI NUMBERS OF THE SECOND KIND", 대한수학회보, 52(3), pp.987~998 (2015), 대한수학회
  33. Some properties of the Bernoulli numbers of the second kind and their generating function, "F. Qi", ResearchGate, ~ (2017)
  34. Feng Qi, "Closed forms for derangement numbers in terms of the Hessenberg determinants", Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 112(4), pp.933~944 (2018), Springer Nature[DOI]
  35. C. -F. Wei, "Several closed expressions for the Euler numbers", J. Inequal. Appl, 2015, pp.219~ (2015)
  36. J. -L. Zhao, "Derivative polynomials of a function related to the Apostol-Euler and Frobenius-Euler numbers", J. Nonlinear Sci. Appl, 10(4), pp.1345~1349 (2017)

관련 논문AI추천

SOME IDENTITIES FOR BERNOULLI NUMBERS OF THE SECOND KIND ARISING FROM A NON-LINEAR DIFFERENTIAL EQUATION김대산, 김태균대한수학회 · 대한수학회보2015 · 제52권 제6호DIFFERENTIAL EQUATIONS ARISING FROM THE GENERATING FUNCTION OF DEGENERATE BERNOULLI NUMBERS OF THE SECOND KIND김대산, 김태균, 장관우, Dmitry V. Dolgy장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2018 · 제21권 제3호DIFFERENTIAL EQUATIONS ARISING FROM STIRLING POLYNOMIALS AND APPLICATIONS권혁인, 김대산, 김태균, 서종진, 장이채장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2016 · 제19권 제2호Some identities of the type 2 degenerate Bernoulli and Euler numbers권종겸, 김대산, 장관우, 정세교장전수학회 · Advanced Studies in Contemporary Mathematics2019 · 제29권 제4호Formulas and relations for Bernoulli-type numbers and polynomials derive from Bessel functionSelin Selen Ozbek Simsek, Yilmaz Simsek대한수학회 · 대한수학회논문집2023 · 제38권 제4호Some closed formulas for generalizations of Bernoulli and Euler numbers and polynomialsH. Yang, Z. Zhang장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2008 · 제11권 제2호

이 간행물의 다른 논문 (21건)

Skew cyclic codes over $\mathbb{F}_p+v\mathbb{F}_p+v^2\mathbb{F}_p$Ahmad Moussavi, Hamed Mousavi, Saeed Rahimipp. 1627-1638Nonlocal boundary value problems for Hilfer fractional differential equationsSuphawat Asawasamrit, Atthapol Kijjathanakorn, Sotiris K. Ntouyas, Jessada Tariboonpp. 1639-1657On a Waring-Goldbach problem involving squares, cubes and biquadratesYuhui Liupp. 1659-1666On the minimum order of 4-lazy cops-win graphsKai An Sim, Kok Bin Wong, Ta Sheng Tanpp. 1667-1690On the location of eigenvalues of real constant row-sum matricesRachid Marsli, Frank J. Hallpp. 1691-1701
원문 보기