Results 201 to 210 of about 233,365 (231)

On the Difference of Orthonormal Polynomials

Quaestiones Mathematicae, 2003
We establish an estimate on the difference of orthonormal polynomials for a general class of exponential weights. Mathematics Subject Classification (2000): 41A05, 05E35, 41A65 Key words: Orthonormal polynomials, exponential weights Quaestiones Mathematicae 26(2003), 347 ...
Kubayi D.G., Mashele H.P.
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Difference polynomials and their generalizations

Mathematika, 2001
\textit{A. Ehrenfeucht} [Pr. Mat. 2, 167--169 (1956; Zbl 0074.25505)] proved that a difference polynomial \(f(X)-g(Y)\) in two variables \(X,Y\) with complex coefficients is irreducible provided that the degrees of \(f\) and \(g\) are coprime. \textit{G. Angermüller} [A generalization of Ehrenfeucht's irreducibility criterion. J.
Sudesh K. Khanduja, Saurabh Bhatia
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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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Remarks on Difference-Polynomials

Bulletin of the London Mathematical Society, 1985
A polynomial of the form \(f(x)-g(y),\) where x and y are disjoint finite sets of variables, is called a difference polynomial. Let \(P(x)-Q(y)\) and \(P^*(x)-Q^*(y)\) be two difference-polynomials having an irreducible common factor F. The main theorem of this article establishes the existence of a difference polynomial f(x)-g(y) which is divisible by
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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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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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Characterization of polynomials and divided difference

Proceedings of the Indian Academy of Sciences - Section A, 1995
The authors offer two additional proofs of a result by \textit{J. Schwaiger} [Aequationes Math. 48, No. 2-3, 317-323 (1994; Zbl 0810.39007)] that the \((n-1)\)-st divided difference (with variable spans) of \(f\) is a function of the sum of its \(n\) variables iff \(f\) is a polynomial of degree at most \(n\); and \(g\) is linear.
Prasanna K. Sahoo, Pl. Kannappan
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On the difference of successive Gaussian polynomials

Journal of Statistical Planning and Inference, 1993
Let \(M,N\in\mathbb{Z}\); as usual, define the ``Gaussian polynomials'' by \({N\brack M}=\prod^ M_ 1(1-q^{N+1-j})\) \((1-q^ j)^{-1}\), if \(0\leq M\leq N\). Otherwise, put \({N\brack M}=0\). According to the author's introduction, ``the object in this paper is to relate differences of Gaussian polynomials to partitions through the use of Frobenius ...
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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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Conversion of Polynomials between Different Polynomial Bases [PDF]

IMA Journal of Numerical Analysis, 1981
Y. L. Luke, B. Y. Ting
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