Results 61 to 70 of about 601,525 (187)
Polynomial solutions of differential–difference equations
Journal of Approximation Theory, 2011 We investigate the zeros of polynomial solutions to the differential-difference equation \[ P_{n+1}(x)=A_{n}(x)P_{n}^{\prime}(x)+B_{n}(x)P_{n}(x), n=0,1,... \] where $A_{n}$ and $B_{n}$ are polynomials of degree at most 2 and 1 respectively. We address the question of when the zeros are real and simple and whether the zeros of polynomials of adjacent ...
Dominici, Diego +2 more
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Some Results on the Deficiencies of Some Differential-Difference Polynomials of Meromorphic Function
Mathematics, 2018 For a transcendental meromorphic function f ( z ) , the main aim of this paper is to investigate the properties on the zeros and deficiencies of some differential-difference polynomials.
Hong-Yan Xu, Xiu-Min Zheng, Hua Wang
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Asymptotically polynomial solutions of difference equations of neutral type
, 2014 Asymptotic properties of solutions of difference equation of the form \[ \Delta^m(x_n+u_nx_{n+k})=a_nf(n,x_{\sigma(n)})+b_n \] are studied. We give sufficient conditions under which all solutions, or all solutions with polynomial growth, or all ...
Migda, Janusz
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On a Difference Equation for Generalizations of Charlier Polynomials
Journal of Approximation Theory, 1995 11 ...
H. Bavinck, Roelof Koekoek
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Mathematics, 2019 By using the Kolmogorov-Arnold-Moser (KAM) theory, we investigate the stability of two elliptic equilibrium points (zero equilibrium and negative equilibrium) of the difference equation t n + 1 = α t n + β t n 2 − t n ...
Tarek F. Ibrahim, Zehra Nurkanović
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An exact formula for general spectral correlation function of random Hermitian matrices
, 2003 We have found an exact formula expressing a general correlation function containing both products and ratios of characteristic polynomials of random Hermitian matrices. The answer is given in the form of a determinant.
Akemann G +29 more
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Difference Sets and Polynomials
, 2015 We provide upper bounds on the largest subsets of $\{1,2,\dots,N\}$ with no differences of the form $h_1(n_1)+\cdots+h_{\ell}(n_{\ell})$ with $n_i\in \mathbb{N}$ or $h_1(p_1)+\cdots+h_{\ell}(p_{\ell})$ with $p_i$ prime, where $h_i\in \mathbb{Z}[x]$ lie in in the classes of so-called intersective and $\mathcal{P}$-intersective polynomials, respectively.
Lyall, Neil, Rice, Alex
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Value distribution of difference polynomials of meromorphic functions
Electronic Journal of Differential Equations, 2013 In this article, we study the value distribution of difference polynomials of meromorphic functions, and obtain some results which can be viewed as discrete analogues of the results given by Yi and Yang [11].
Yong Liu, Xiaoguang Qi, Hongxun Yi
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Asymptotic iteration method for solving Hahn difference equations
Advances in Difference Equations, 2021 Hahn’s difference operator D q ; w f ( x ) = ( f ( q x + w ) − f ( x ) ) / ( ( q − 1 ) x + w ) $D_{q;w}f(x) =({f(qx+w)-f(x)})/({(q-1)x+w})$ , q ∈ ( 0 , 1 ) $q\in (0,1)$ , w > 0 $w>0$ , x ≠ w / ( 1 − q ) $x\neq w/(1-q)$ is used to unify the recently ...
Lucas MacQuarrie +2 more
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Algorithms for integrals of holonomic functions over domains defined by polynomial inequalities
, 2011 We present an algorithm for computing a holonomic system for a definite integral of a holonomic function over a domain defined by polynomial inequalities.
Almkvist +25 more
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