Results 11 to 20 of about 173,713 (336)
Bernoulli Numbers and Solitons [PDF]
Journal of Nonlinear Mathematical Physics, 2005 We present a new formula for the Bernoulli numbers as the following integral $$B_{2m} =\frac{(-1)^{m-1}}{2^{2m+1}} \int_{-\infty}^{+\infty} (\frac{d^{m-1}}{dx^{m-1}} {sech}^2 x)^2dx. $$ This formula is motivated by the results of Fairlie and Veselov, who discovered the relation of Bernoulli polynomials with soliton theory.
Grosset, Marie-Pierre +1 more
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Electronic Research Archive, 2023 In this paper, a fractional opposite-direction accumulating nonlinear grey Bernoulli Markov model (FOANGBMKM) is established to forecast the annual GDP of Huizhou city from 2017 to 2021. The optimal fractional order number and nonlinear parameters of the
Meilan Qiu +3 more
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Sums involving the binomial coefficients, Bernoulli numbers of the second kind and harmonic numbers [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 We offer a number of various finite and infinite sum identities involving the binomial coefficients, Bernoulli numbers of the second kind and harmonic numbers. For example, among many others, we prove Σⁿₖ₌ₒ((-1)ᵏhₖ/4ᵏ)$binom{2k}{k}$Gₙ₋ₖ = ((-1)ⁿ⁻¹/2^²ⁿ⁻¹)
Necdet Batır, Anthony Sofo
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Extended Bernoulli and Stirling matrices and related combinatorial identities [PDF]
, 2013 In this paper we establish plenty of number theoretic and combinatoric identities involving generalized Bernoulli and Stirling numbers of both kinds. These formulas are deduced from Pascal type matrix representations of Bernoulli and Stirling numbers ...
Can, Mümün, Dağlı, M. Cihat
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Congruences among generalized Bernoulli numbers [PDF]
Acta Arithmetica, 1995 Let \(\chi\) denote a primitive quadratic character mod \(M\) (or the trivial character) and let \(d\) be a fundamental discriminant (or 1). Denote by \(\chi'\) the character mod \(M |d |\) induced by \(\chi\). The authors consider the generalized Bernoulli numbers \(B_{m, \chi'}\) and the corresponding Bernoulli polynomials \(B_{m, \chi'} (X)\) at \(X
Szmidt, J. +2 more
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Fungsi Zeta Riemann Genap Menggunakan Bilangan Bernoulli
Desimal, 2019 In this article, we study about the value of Riemann Zeta Function for even numbers using Bernoulli number. First, we give some basic theory about Bernoulli number and Riemann Zeta function.
Ikhsan Maulidi +2 more
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New inequalities of Wilker’s type for circular functions
AIMS Mathematics, 2020 In the article, we establish three new Wilker type inequalities involving tangent and sine functions by use of a double inequality for the ratio of two consecutive non-zero Bernoulli numbers.
Ling Zhu
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q-Bernoulli numbers and q-Bernoulli polynomials revisited [PDF]
Advances in Difference Equations, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kim Taekyun, Lee Byungje, Ryoo Cheon
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Generalized degenerate Bernoulli numbers and polynomials arising from Gauss hypergeometric function
Advances in Difference Equations, 2021 A new family of p-Bernoulli numbers and polynomials was introduced by Rahmani (J. Number Theory 157:350–366, 2015) with the help of the Gauss hypergeometric function.
Taekyun Kim +4 more
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Mathematics, 2020 In this paper, we define cosine Bernoulli polynomials and sine Bernoulli polynomials related to the q-number. Furthermore, we intend to find the properties of these polynomials and check the structure of the roots.
Jung Yoog Kang, Chen Seoung Ryoo
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