Results 221 to 230 of about 726,471 (254)

Convolutions of Bernoulli and Euler Polynomials

Sarajevo Journal of Mathematics
By means of the generating function technique, several convolution identities are derived for the polynomials of Bernoulli and Euler.   2000 Mathematics Subject Classification.
CHU, Wenchang, ZHOU R. R.
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A New Formula for the Bernoulli Polynomials

Results in Mathematics, 2010
The author defines \(r\)-Whitney numbers \(w_{m,r}(n,k)\) and \(W_{m,r}(n,k)\) of the first and second kind by the equalities \[ m^nx^{\underline{n}}=\sum_{k=0}^nw_{m,r}(n,k)(mx+r)^k \] and \[ (mx+r)^n=\sum_{k=0}^nm^kW_{m,r}(n,k)x^{\underline{k}} \] with \(x^{\underline{n}}=x(x-1)\cdots(x-n+1)\) denoting falling factorials. These numbers are also given
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Convolution and Reciprocity Formulas for Bernoulli Polynomials

Integers, 2011
AbstractWe prove a new convolution identity for sums of products of two Bernoulli polynomials. This can be rewritten to obtain a reciprocity relation for a related sum. The proof uses some results on Stirling numbers of both kinds which are of independent interest. In particular, a class of polynomials related to the Stirling numbers of the second kind
Takashi Agoh, Karl Dilcher
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Probabilistic Bernoulli and Euler Polynomials

Russian Journal of Mathematical Physics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kim, T., Kim, D. S.
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q-Analogs of Lidstone expansion theorem, two-point Taylor expansion theorem, and Bernoulli polynomials

Analysis and Applications, 2019
In this paper, we introduce a generalization of the [Formula: see text]-Taylor expansion theorems. We expand a function in a neighborhood of two points instead of one in three different theorems.
M. Ismail, Z. Mansour
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Formulas for Bernoulli Numbers and Polynomials

Results in Mathematics
Special polynomials and numbers possess much importance in multifarious areas of sciences such as physics, mathematics, applied sciences, engineering, and other related research fields covering differential equations, number theory, functional analysis, quantum mechanics, mathematical analysis, mathematical physics, and so on.
Ulrich Abel, Horst Alzer
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New formulation of the orthonormal Bernoulli polynomials for solving the variable-order time fractional coupled Boussinesq–Burger’s equations

Engineering computations, 2020
M. Heydari, Z. Avazzadeh
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Explicit Formulas for Probabilistic Multi-Poly-Bernoulli Polynomials and Numbers

Russian journal of mathematical physics
T. Kim, D. Kim
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Explicit representation of orthonormal Bernoulli polynomials and its application for solving Volterra–Fredholm–Hammerstein integral equations

SeMA Journal, 2020
Farshid Mirzaee, Nasrin Samadyar
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Some new identities and inequalities for Bernoulli polynomials and numbers of higher order related to the Stirling and Catalan numbers

RACSAM, 2020
Damla Gun, Y. Şimşek
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