Results 21 to 30 of about 592,672 (233)

Exponential Polynomials and Nonlinear Differential-Difference Equations

open access: yesJournal of Function Spaces, 2020
In this paper, we study finite-order entire solutions of nonlinear differential-difference equations and solve a conjecture proposed by Chen, Gao, and Zhang when the solution is an exponential polynomial.
Junfeng Xu, Jianxun Rong
doaj   +1 more source

Orthogonal Polynomials with Singularly Perturbed Freud Weights

open access: yesEntropy, 2023
In this paper, we are concerned with polynomials that are orthogonal with respect to the singularly perturbed Freud weight functions. By using Chen and Ismail’s ladder operator approach, we derive the difference equations and differential-difference ...
Chao Min, Liwei Wang
doaj   +1 more source

On the ω-multiple Meixner polynomials of the first kind

open access: yesJournal of Inequalities and Applications, 2020
In this study, we introduce a new family of discrete multiple orthogonal polynomials, namely ω-multiple Meixner polynomials of the first kind, where ω is a positive real number.
Sonuç Zorlu Oğurlu, İlkay Elidemir
doaj   +1 more source

Algebra of quantum C $$ \mathcal{C} $$ -polynomials

open access: yesJournal of High Energy Physics, 2021
Knot polynomials colored with symmetric representations of SL q (N) satisfy difference equations as functions of representation parameter, which look like quantization of classical A $$ \mathcal{A} $$ -polynomials.
Andrei Mironov, Alexei Morozov
doaj   +1 more source

On the difference between permutation polynomials

open access: yesFinite Fields and Their Applications, 2018
Abstract The well-known Chowla and Zassenhaus conjecture, proved by Cohen in 1990, states that if p > ( d 2 − 3 d + 4 ) 2 , then there is no complete mapping polynomial f in F p [ x ] of degree d ≥ 2 .
Vandita Patel   +6 more
openaire   +4 more sources

Multivariate difference Gončarov polynomials

open access: yes, 2022
17 ...
Adeniran, A., Snider, L., Yan, C.
openaire   +2 more sources

On the Finite Differences of a Polynomial [PDF]

open access: yesThe Annals of Mathematical Statistics, 1935
In this paper an apparently new and convenient method of finding the successive finite differences of a polynomial is considered. If operationally 4(u + rjr2) = Er7r2 4(u) = (1 + Ari)r2 4o(u) then for any polynomial f(x) of degree "n" f(x) = po xn + P, Xn-1 +--+ Pn = po(x + a)n + qll(x + a)n-I + + qln Eaf(x) = po(x + a)n + pl(x + a)n-' + + Pn Aaf(X) = (
openaire   +2 more sources

Polynomial solutions of algebraic difference equations and homogeneous symmetric polynomials

open access: yesJournal of Symbolic Computation, 2021
This article addresses the problem of computing an upper bound of the degree d of a polynomial solution P(x) of an algebraic difference equation of the form G(x)(P(x−τ1),…,P(x−τs))+G0(x)=0 when such P(x) with the coefficients in a field K of characteristic zero exists and where G is a non-linear s-variable polynomial with coefficients in K[x] and G0 is
Olha Shkaravska   +3 more
openaire   +4 more sources

Zeros of some difference polynomials [PDF]

open access: yesAdvances in Difference Equations, 2013
In this paper, we study zeros of some difference polynomials in f (z) and their shifts, where f (z) is a finite order meromorphic function having deficient value ∞. These results improve previous findings.
Zong-Xuan Chen, Shuangting Lan
openaire   +2 more sources

Unicity of transcendental meromorphic functions concerning differential-difference polynomials

open access: yesAIMS Mathematics, 2022
Let $ f $ and $ g $ be two transcendental meromorphic functions of finite order with a Borel exceptional value $ \infty $, let $ \alpha $ $ (\not\equiv 0) $ be a small function of both $ f $ and $ g $, let $ d, k, n, m $ and $ v_j (j = 1, 2, \cdots, d) $
Zhiying He, Jianbin Xiao, Mingliang Fang
doaj   +1 more source

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