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Uniqueness of difference polynomials
AIMS Mathematics, 2021 Let $ f(z) $ be a transcendental meromorphic function of finite order and $ c\in\Bbb{C} $ be a nonzero constant. For any $ n\in\Bbb{N}^{+} $, suppose that $ P(z, f) $ is a difference polynomial in $ f(z) $ such as $ P(z, f) = a_{n}f(z+nc)+a_{n-1}f(z+(n-1)
Xiaomei Zhang , Xiang Chen
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Manifolds of Difference Polynomials [PDF]
Transactions of the American Mathematical Society, 1948 1. It is the purpose of this paper to develop in some detail the structure of the manifolds determined by systems of difference polynomials. Our results will necessarily be confined to the case of polynomials in an abstract field, since a suitable existence theorem for analytic difference equations is not available. The ideal theory, developed by J. F.
Richard M. Cohn
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Mathematics, 2023 In this review paper, our aim is to study the current research progress of q-difference equations for generalized Al-Salam–Carlitz polynomials related to theta functions and to give an extension of q-difference equations for q-exponential operators and q-
Jian Cao +3 more
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Discrete Hypergeometric Legendre Polynomials
Mathematics, 2021 A discrete analog of the Legendre polynomials defined by discrete hypergeometric series is investigated. The resulting polynomials have qualitatively similar properties to classical Legendre polynomials.
Tom Cuchta, Rebecca Luketic
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Sharing values of q-difference-differential polynomials
Advances in Difference Equations, 2020 This paper is devoted to the uniqueness of q-difference-differential polynomials of different types. Using the idea of common zeros and common poles (Chin. Ann. Math., Ser.
Jian Li, Kai Liu
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A NEW CHARACTERIZATION OF SYMMETRIC DUNKL AND \(q\)-DUNKL-CLASSICAL ORTHOGONAL POLYNOMIALS
Ural Mathematical Journal, 2023 In this paper, we consider the following \(\mathcal{L}\)-difference equation $$\Phi(x) \mathcal{L}P_{n+1}(x)=(\xi_nx+\vartheta_n)P_{n+1}(x)+\lambda_nP_{n}(x),\quad n\geq0,$$where \(\Phi\) is a monic polynomial (even), \(\deg\Phi\leq2\), \(\xi_n ...
Yahia Habbachi
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Zeros of difference polynomials
Journal of Approximation Theory, 1992 Studies --- both analytic and numerical --- on polynomials have been of immense interest for long. Here the authors deal in detail with various questions relating to the zeros of difference polynomials. Particularly, defining the difference operator by \(\Delta f(x)=f(x+1)-f(x)\), the polynomial \(\Delta^ mx^ n\) of degree \((n-m)\) having \((n-m ...
John J. Warvik, Ronald J. Evans
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Polynomial Differences in the Primes [PDF]
, 2014 We establish, utilizing the Hardy-Littlewood Circle Method, an asymptotic formula for the number of pairs of primes whose differences lie in the image of a fixed polynomial. We also include a generalization of this result where differences are replaced with any integer linear combination of two primes.
Alex Rice, Neil Lyall
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On the Uniqueness Results and Value Distribution of Meromorphic Mappings
Mathematics, 2017 This research concentrates on the analysis of meromorphic mappings. We derived several important results for value distribution of specific difference polynomials of meromorphic mappings, which generalize the work of Laine and Yang.
Rahman Ullah +4 more
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A high order $q$-difference equation for $q$-Hahn multiple orthogonal polynomials [PDF]
, 2009 A high order linear $q$-difference equation with polynomial coefficients having $q$-Hahn multiple orthogonal polynomials as eigenfunctions is given. The order of the equation is related to the number of orthogonality conditions that these polynomials ...
Abramowitz M. +10 more
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