Results 21 to 30 of about 10,388 (168)
q-Bernoulli Numbers Associated with q-Stirling Numbers
Advances in Difference Equations, 2008 We consider Carlitz q-Bernoulli numbers and q-Stirling numbers of the first and the second kinds. From the properties of q-Stirling numbers, we derive many interesting formulas associated with Carlitz q-Bernoulli numbers. Finally, we will prove βn,q=â
Taekyun Kim
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Demonstratio Mathematica, 2022 In this article, the authors present two identities involving products of the Bernoulli numbers, provide four alternative proofs for these two identities, derive two closed-form formulas for the Bernoulli numbers in terms of central factorial numbers of ...
Chen Xue-Yan +3 more
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Advances in Difference Equations, 2010 We define the twisted q-Bernoulli polynomials and the twisted generalized q-Bernoulli polynomials attached to χ of higher order and investigate some symmetric properties of them. Furthermore, using these symmetric properties of them, we can obtain
L.-C. Jang +5 more
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Journal of Number Theory, 1995 The author strengthens the Sylvester-Lipschitz theorem for Bernoulli numbers \(B_m\) as follows: ``For an integer \(a\) and a positive integer \(m\) the number \(a^{[\log_2 m]+1} (a^m- 1)B_m/ m\) is an integer.'' It is noted that in a certain sense this strengthening of the Sylvester- Lipschitz theorem is the best possible.
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Bernoulli Related Polynomials and Numbers [PDF]
Mathematics of Computation, 1979 The polynomials φ
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Explicit Formulas Involving -Euler Numbers and Polynomials
Abstract and Applied Analysis, 2012 We deal with -Euler numbers and -Bernoulli numbers. We derive some interesting relations for -Euler numbers and polynomials by using their generating function and derivative operator.
Serkan Araci +2 more
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Mathematics, 2021 In this paper, we further study the generating function involving a variety of special numbers and ploynomials constructed by the second author. Applying the Mellin transformation to this generating function, we define a new class of zeta type functions,
Daeyeoul Kim, Yilmaz Simsek
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Fully degenerate poly-Bernoulli numbers and polynomials
Open Mathematics, 2016 In this paper, we introduce the new fully degenerate poly-Bernoulli numbers and polynomials and inverstigate some properties of these polynomials and numbers.
Kim Taekyun, Kim Dae San, Seo Jong-Jin
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Journal of Inequalities and Applications, 2018 In the present paper, firstly we find a number of poles of generating functions of Bernoulli numbers and associated Euler numbers, denoted by n(a,B) $n ( a,\mathbf{B} ) $ and n(a,E) $n ( a,E ) $, respectively.
Serkan Araci, Mehmet Acikgoz
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