Results 21 to 30 of about 592,672 (233)
Exponential Polynomials and Nonlinear Differential-Difference Equations
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
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Orthogonal Polynomials with Singularly Perturbed Freud Weights
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
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On the ω-multiple Meixner polynomials of the first kind
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
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Algebra of quantum C $$ \mathcal{C} $$ -polynomials
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
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On the difference between permutation polynomials
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
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Multivariate difference Gončarov polynomials
17 ...
Adeniran, A., Snider, L., Yan, C.
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On the Finite Differences of a Polynomial [PDF]
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) = (
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Polynomial solutions of algebraic difference equations and homogeneous symmetric polynomials
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
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Zeros of some difference polynomials [PDF]
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
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Unicity of transcendental meromorphic functions concerning differential-difference polynomials
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
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