Results 121 to 130 of about 1,563 (216)

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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p-Bernoulli and geometric polynomials

, 2018
We relate geometric polynomials and [Formula: see text]-Bernoulli polynomials with an integral representation, then obtain several properties of [Formula: see text]-Bernoulli polynomials.
Levent Kargın
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Bernoulli polynomials [PDF]

, 2018
U ovome radu prezentirana su neka osnovna svojstva Bernoullijevih brojeva i Bernoullijevih polinoma. Razmatrane su primjene Bernoullijevih brojeva i Bernoullijevih polinoma pri računanju suma potencija prvih n prirodnih brojeva, pri razvoju funkcija u ...
Mihaela Ribičić Penava, Nuić, Antonio, Ribičić Penava, Mihaela, Antonio Nuić   +3 more
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A Note on Symmetric Properties of the Twisted -Bernoulli Polynomials and the Twisted Generalized -Bernoulli Polynomials

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, Yi H, Kim T, Kim YH, Shivashankara K, Jang L-C   +5 more
doaj  

Formulas Involving Cauchy Polynomials, Bernoulli Polynomials, and Generalized Stirling Numbers of Both Kinds

Axioms
In 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
doaj   +1 more source

Velocity field and cavity dynamics in drop impact experiments. [PDF]

J Fluid Mech, 2023
Lherm V, Deguen R.
europepmc   +1 more source

Simple Equations Method (SEsM): An Effective Algorithm for Obtaining Exact Solutions of Nonlinear Differential Equations. [PDF]

Entropy (Basel), 2022
Vitanov NK.
europepmc   +1 more source

Explicit values of Bernoulli polynomials at rational numbers

Journal of Mathematical Analysis and Applications
The 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, Lerna Pehlivan, Kenneth S. Williams   +2 more
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CONVOLUTION THEOREMS FOR HYPERGEOMETRIC BERNOULLI NUMBERS AND POLYNOMIALS

, 2023
In this paper, we study hypergeometric Bernoulli numbers and polynomials and userecurrence relations to generate higher order convolution identities involving the sums of theseBernoulli numbers. We consider cases where the Bernoulli number/polynomial are
R. Ernst , Christopher, Hassen, Abdul
core  

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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