Results 281 to 290 of about 17,850 (309)

Multivariable Difference Dimension Polynomials

Journal of Mathematical Sciences, 2005
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Singular Manifolds of Difference Polynomials

The Annals of Mathematics, 1951
1. Let F be an algebraically irreducible difference polynomial in unknowns Y1, Y2, ... , yn with coefficients in a difference field W. We showed previously' that the irreducible components of the manifold of F are of two types: ordinary manifolds not held by any polynomial of lower effective order than F in any yj; and essential singular manifolds ...
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Finite Differences and Orthogonal Polynomials

The Ramanujan Journal, 1999
By combining finite differences with symmetric functions, we present an elementary demonstration for the limit relation from Laguerre to Hermite polynomials, proposed by Richard Askey. Another limit relation between these two polynomials is also established.
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On properties of difference polynomials

Acta Mathematica Scientia, 2011
Abstract We study the value distribution of difference polynomials of meromorphic functions, and extend classical theorems of Tumura-Clunie type to difference polynomials. We also consider the value distribution of f(z)f(z+c) .
Chen Zongxuan, Huang Zhibo, Zheng Xiumin
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Polynomials and divided differences

Publicationes Mathematicae Debrecen, 2005
\textit{J. Aczél} showed in 1963 [see Math. Mag. 58, 42--45 (1985; Zbl 0571.39005)] that there is a simple functional equation involving two unknown functions, say \(f\) and \(g\), whose general solution (no regularity conditions whatever) is: \(f\) is a polynomial of degree at most 2 and \(g\) is the derivative of \(f\).
Riedel, Thomas, Sablik, Maciej, Sklar, Abe   +2 more
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Elimination theory for differential difference polynomials

Proceedings of the 2003 international symposium on Symbolic and algebraic computation, 2003
In this paper we give an elimination algorithm for differential difference polynomial systems. We use the framework of a generalization of Ore algebras, where the independent variables are non-commutative. We prove that for certain term orderings, Buchberger's algorithm applied to differential difference systems terminates and produces a Grobner basis.
Elizabeth L. Mansfield, Ágnes Szántó
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Relating Different Polynomial-LWE Problems

2019
In this paper we focus on Polynomial Learning with Errors (PLWE). This problem is parametrized by a polynomial and we are interested in relating the hardness of the \(\text {PLWE}^f\) and \(\text {PLWE}^h\) problems for different polynomials f and h.
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Conversion of Polynomials between Different Polynomial Bases

IMA Journal of Numerical Analysis, 1981
Ting, B. Y., Luke, Y. L.
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A Review of q-Difference Equations for Al-Salam–Carlitz Polynomials and Applications to U(n + 1) Type Generating Functions and Ramanujan’s Integrals

Mathematics, 2023
Jian Cao, MOHAMMED FADEL, Sama Arjika
exaly  

A q-Difference Equation and Fourier Series Expansions of q-Lidstone Polynomials

Symmetry, 2022
Maryam Al-Towailb
exaly