Results 91 to 100 of about 174,275 (197)

An Extension of the Hilbert's Integral Inequality

Journal of Inequalities and Applications, 2009
It is shown that an extension of the Hilbert's integral inequality can be established by introducing two parameters m   (m∈N) and λ   (λ>0).
Zhou Yu, Gao Xuemei, Gao Mingzhe
doaj   +1 more source

Extension of the Bernoulli and Eulerian Polynomials of Higher Order and Vector Partition Function

, 2006
Following the ideas of L. Carlitz we introduce a generalization of the Bernoulli and Eulerian polynomials of higher order to vectorial index and argument. These polynomials are used for computation of the vector partition function $W({\bf s},{\bf D})$, i.
Rubinstein, Boris Y.
core  

On Carlitz's q-Bernoulli numbers

Journal of Number Theory, 1982
Bernoulli numbers and polynomials can be used to define \(p\)-adic analogues of the classical zeta function and \(L\)-functions (as an integral of a simple function with respect to a measure that is a regularization of a Bernoulli distribution, see [the author, \(p\)-adic numbers, \(p\)-adic analysis, and zeta-functions.
openaire   +1 more source

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.
openaire   +2 more sources

Joint distribution for number of crossings and longest run in independent Bernoulli observations. The R package crossrun.

PLoS ONE, 2019
The R package crossrun computes the joint distribution of the number of crossings and the longest run in a sequence of independent Bernoulli observations.
Tore Wentzel-Larsen, Jacob Anhøj
doaj   +1 more source

Probabilistic poly-Bernoulli numbers

Mathematical and Computer Modelling of Dynamical Systems
Assume that is Y a random variable whose moment generating function exists in a neighbourhood of the origin. The aim of this paper is to study probabilistic poly-Bernoulli numbers associated with Y, as probabilistic extensions of poly-Bernoulli numbers.
Wencong Liu, Yuankui Ma, Taekyun Kim, Dae San Kim   +3 more
openaire   +2 more sources

Exploring probabilistic Bernstein polynomials: identities and applications

Applied Mathematics in Science and Engineering
In this paper, we introduce the probabilistic Bernstein polynomials and derive new and interesting correlations among several special functions and special number sequences such as Euler polynomials, Bernoulli polynomials of higher order, Frobenius–Euler
Ayse Karagenc, Mehmet Acikgoz, Serkan Araci   +2 more
doaj   +1 more source

An Upper Bound for Locating Strings with High Probability Within Consecutive Bits of Pi

Mathematics
Numerous studies on the number pi (π) explore its properties, including normality and applicability. This research, grounded in two hypotheses, proposes and proves a theorem that employs a Bernoulli experiment to demonstrate the high probability of ...
Víctor Manuel Silva-García, Manuel Alejandro Cardona-López, Rolando Flores-Carapia   +2 more
doaj   +1 more source

Fibonacci Sums Modulo 5

Annales Mathematicae Silesianae
We develop closed form expressions for various finite binomial Fibonacci and Lucas sums depending on the modulo 5 nature of the upper summation limit. Our expressions are inferred from some trigonometric identities.
Adegoke Kunle, Frontczak Robert, Goy Taras   +2 more
doaj   +1 more source

An efficient coupled polynomial interpolation scheme to eliminate material-locking in the Euler-Bernoulli piezoelectric beam finite element

Latin American Journal of Solids and Structures
The convergence characteristic of the conventional two-noded Euler-Bernoulli piezoelectric beam finite element depends on the configuration of the beam cross-section.
Litesh N. Sulbhewar, P. Raveendranath
doaj   +1 more source