Results 111 to 120 of about 18,359 (203)
On the theory of the Bernoulli polynomials and numbers
Journal of Mathematical Analysis and Applications, 1984 This is an excellent paper containing several new representations of the Bernoulli polynomials and the Bernoulli numbers. In the sequel, let \(n\) be any nonnegative integer unless otherwise specified, and let \(S(n,k)\) be the Stirling numbers of the second kind.
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Velocity field and cavity dynamics in drop impact experiments. [PDF]
J Fluid Mech, 2023 Lherm V, Deguen R.
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A generalization of the Bernoulli polynomials
Journal of Applied Mathematics, 2003 A generalization of the Bernoulli polynomials and, consequently, of the Bernoulli numbers, is defined starting from suitable generating functions. Furthermore, the differential equations of these new classes of polynomials are derived by means of the ...
Pierpaolo Natalini, Angela Bernardini
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The Powers Sums, Bernoulli Numbers, Bernoulli Polynomials Rethinked
Applied Mathematics, 2019 Utilizing translation operators we get the powers sums on arithmetic progressions and the Bernoulli polynomials of order munder the form of differential operators acting on monomials. It follows that (d/dn-d/dz) applied on a power sum has a meaning and is exactly equal to the Bernoulli polynomial of the same order.
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Advances in Difference Equations, 2010 We define the twisted -Bernoulli polynomials and the twisted generalized -Bernoulli polynomials attached to of higher order and investigate some symmetric properties of them.
Lee B +5 more
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AxiomsIn this paper, we derive novel formulas and identities connecting Cauchy numbers and polynomials with both ordinary and generalized Stirling numbers, binomial coefficients, central factorial numbers, Euler polynomials, r-Whitney numbers, and ...
José L. Cereceda
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Simple Equations Method (SEsM): An Effective Algorithm for Obtaining Exact Solutions of Nonlinear Differential Equations. [PDF]
Entropy (Basel), 2022 Vitanov NK.
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Explicit values of Bernoulli polynomials at rational numbers
Journal of Mathematical Analysis and ApplicationsThe content of the paper covers the following topics the Bernoulli polynomials and numbers, the Riemann zeta and the Hurwitz zeta functions, and Lehmer's question. The authors give many relations and formulas in order to evaluate values of the Bernoulli polynomials at rational numbers.
Florian Münkel +2 more
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A note on Bernoulli numbers and polynomials
, 1974 Put \(S_k =S_k(n) = \sum_{n=0}^{n-1} a^k\). It is well known that \(S_1^2 = S_3\), \(2S_1^4 = S_5 + S_7\). Stern showed that [\textit{P. Bachmann}, Niedere Zahlentheorie. Tell II (Teubner, Leipzig, 1910, p. 20) (reprint Chelsea, Bronx, 1968; Zbl. 253.10001)) \[ 2^{m-1} S_1^m = \sum_{2j < m} \binom{m}{2j+1} S_{2m-2j-1}.
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Selection of Radial Basis Functions for the Accuracy of Meshfree Galerkin Method in Rotating Euler-Bernoulli Beam Problem. [PDF]
Int J Appl Comput Math, 2022 Panchore V.
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