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A NOTE ON SOME IDENTITIES OF BERNOULLI NUMBERS ARISING FROM RIEMANN INTEGRALS
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초록
In this paper, we represent the generating function of Bernoulli numbers and its reciprocal as Riemann integrals on the unit interval. From these integral representations and in an elementary way, we derive several identities involving Bernoulli numbers, Bell numbers and Stirling nubers of the first and second kinds.
Abstract
In this paper, we represent the generating function of Bernoulli numbers and its reciprocal as Riemann integrals on the unit interval. From these integral representations and in an elementary way, we derive several identities involving Bernoulli numbers, Bell numbers and Stirling nubers of the first and second kinds.
참고문헌 (13)
- 장관우, "Some identities of central Fubini polynomials arising from nonlinear differential equation", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 22(2), pp.205~214 (2019), 장전수학회
- 김대산, "TWO VARIABLE HIGHER-ORDER DEGENERATE FUBINI POLYNOMIALS", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 21(1), pp.5~22 (2018), 장전수학회[DOI]
- Kim, D. S, "Some identities of Bell polynomials", Sci. China Math, 58(10), pp.2095~2104 (2015)
- 김대산, "Two variable higher-order Fubini polynomials", 대한수학회지, 55(4), pp.975~986 (2018), 대한수학회
- 김대산, "A note on $lanbda$-Bernoulli numbers of the second kind", Advanced Studies in Contemporary Mathematics, 30(2), pp.187~196 (2020), 장전수학회
- 김대산, "GENERALIZED TYPE 2 DEGENERATE EULER NUMBERS", Advanced Studies in Contemporary Mathematics, 30(2), pp.166~169 (2020), 장전수학회
- 김태균, "ON CENTRAL FUBINI POLYNOMIALS ASSOCIATED WITH CENTRAL FACTORIAL NUMBERS OF THE SECOND KIND", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 21(4), pp.589~598 (2018), 장전수학회[DOI]
- 김태균, "λ-analogue of stirling numbers of the first kind", Advanced Studies in Contemporary Mathematics, 27(3), pp.423~429 (2017), 장전수학회[DOI]
- 김택연, "A NOTE ON DEGENERATE FUBINI POLYNOMIALS", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 20(4), pp.521~531 (2017), 장전수학회[DOI]
- Kim, T, "Two variable higher-order central Fubini polynomials", J. Inequal. Appl, pp.13~ (2019)
- 마민영, "SOME IDENTITIES ON THE FULLY DEGENERATE BELL POLYNOMIALS OF THE SECOND KIND", Advanced Studies in Contemporary Mathematics, 30(1), pp.145~154 (2020), 장전수학회
- Roman, S, "The umbral calculus. Pure and Applied Mathematics, 111" (1984), Academic Press, Inc
- YILMAZ SIMSEK, "IDENTITIES ON THE CHANGHEE NUMBERS AND APOSTOL-TYPE DAEHEE POLYNOMIALS", Advanced Studies in Contemporary Mathematics, 27(2), pp.199~212 (2017), 장전수학회[DOI]
관련 논문AI추천
AN INTEGRAL REPRESENTATION, SOME INEQUALITIES, AND COMPLETE MONOTONICITY OF THE BERNOULLI NUMBERS OF THE SECOND KINDFeng Qi, Xiao-Jing Zhang대한수학회 · 대한수학회보2015 · 제52권 제3호SOME IDENTITIES FOR BERNOULLI NUMBERS OF THE SECOND KIND ARISING FROM A NON-LINEAR DIFFERENTIAL EQUATION김대산, 김태균대한수학회 · 대한수학회보2015 · 제52권 제6호SOME IDENTITIES INVOLVING FROBENIUS-EULER POLYNOMIALS AND NUMBERS김태균, 서종진장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2016 · 제19권 제1호A note on Eulerian polynomials associated with Bernoulli and Euler numbers and polynomials김대산, 김영희, D. V. Dolgy, T. Kim장전수학회 · Advanced Studies in Contemporary Mathematics2012 · 제22권 제3호ON POLYNOMIALS RELATED TO THE STIRLING NUMBERS AND THE BELL POLYNOMIALS ASSOCIATED WITH p-ADIC INTEGRAL ON Zp이희영장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2016 · 제19권 제4호Bernstein polynomials and Bernoulli numbers유천성장전수학회 · Advanced Studies in Contemporary Mathematics2011 · 제21권 제3호
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