Results 21 to 30 of about 230,209 (328)
On difference polynomials and hereditarily irreducible polynomials
Journal of Number Theory, 1980 AbstractA difference polynomial is one of the form P(x, y) = p(x) − q(y). Another proof is given of the fact that every difference polynomial has a connected zero set, and this theorem is applied to give an irreducibility criterion for difference polynomials. Some earlier problems about hereditarily irreducible polynomials (HIPs) are solved.
Lee A. Rubel, Helge Tverberg, A Schinzel
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Uniqueness on linear difference polynomials of meromorphic functions
AIMS Mathematics, 2021 Suppose that $f(z)$ is a meromorphic function with hyper order $\sigma_{2}(f)
Ran Ran Zhang +2 more
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Exponential Polynomials and Nonlinear Differential-Difference Equations
Journal 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
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On the ω-multiple Meixner polynomials of the first kind
Journal 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
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Orthogonal Polynomials with Singularly Perturbed Freud Weights
Entropy, 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
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, 2020 In this contribution we consider sequences of monic polynomials orthogonal with respect to Sobolev-type inner product \[ \left\langle f,g\right\rangle= \langle {\bf u}^{\tt M},fg\rangle+\lambda \mathscr T^j f (\alpha)\mathscr T^{j}g(\alpha), \] where ...
Costas-Santos, R. S. +2 more
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Algebra of quantum C $$ \mathcal{C} $$ -polynomials
Journal 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
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Matrix-Valued Little q-Jacobi Polynomials [PDF]
, 2014 Matrix-valued analogues of the little q-Jacobi polynomials are introduced and studied. For the 2x2-matrix-valued little q-Jacobi polynomials explicit expressions for the orthogonality relations, Rodrigues formula, three-term recurrence relation and their
Aldenhoven, Noud +2 more
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On the Intersections of the Components of a Difference Polynomial [PDF]
Proceedings of the American Mathematical Society, 1955 The purpose of this note is to prove the following theorem: Solutions common to two distinct components' of the manifold of a difference polynomial annul the separants of the polynomial. We begin by considering a field I, not necessarily a difference field, and a set of polynomials F,, F2,, * * *, Fp in K[ul, * , u.; xl, * *I* xp], the ui and xj being ...
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On the Deficiencies of Some Differential-Difference Polynomials
Abstract and Applied Analysis, 2014 The characteristic functions of differential-difference polynomials are investigated, and the result can be viewed as a differential-difference analogue of the classic Valiron-Mokhon’ko Theorem in some sense and applied to investigate the deficiencies of
Xiu-Min Zheng, Hong Yan Xu
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