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Discrete Invariant Curve Flows, Orthogonal Polynomials, and Moving Frame
, 2020In this paper, an orthogonal polynomials-based (OPs-based) approach to generate discrete moving frames and invariants is developed. It is shown that OPs can provide explicit expressions for the discrete moving frame as well as the associated difference
Bao Wang +3 more
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Hermite Orthogonal Polynomials of a Discrete Variable
Journal of Computational Methods in Sciences and Engineering, 2002The Hermite orthogonal polynomials on a discrete point set are constructed. A discrete point set, a weight function and normalizing factors are obtained, and the orthogonality of them is proved. The problems of an approximation of functions by one, two and three variables with the help of interpolation of the Hermite series constructed on the ...
Streltsova, O. I., Streltsov, I. P.
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Discrete orthogonal matrix polynomials
Analysis Mathematica, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Difference Equations and Discriminants for Discrete Orthogonal Polynomials
The Ramanujan Journal, 2005Let \(\{p_n(x)\}\) be a sequence of discrete orthogonal polynomials satisfy orthogonality relation \[ \sum_{l=s}^t p_m(l)p_n(l)w(l)=\kappa_m \delta_{m,n} \qquad \qquad \sum_{l=s}^t w(l)=1 \] where \(w\) is a weight function. \(l \in \{s, s+1, \dots, t\} \subset \mathbf{R}\), \(s\) is finite but \(t\) is finite or infinite.
M. Ismail, I. Nikolova, P. Simeonov
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Chopped Orthogonal Polynomial Expansions—Some Discrete Cases
SIAM Journal on Algebraic Discrete Methods, 1983We study expansions of functions $f ( x )$ in terms of certain discrete families of orthogonal polynomials, $\{ p_i ( x ) \}$ where $x = 0,1, \cdots ,N,N$ finite or infinite. We assume f is known for $x\leqq M( M < N )$ and that the expansion in terms of the $p_i $’s is chopped after L terms $( L < N )$.
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Second order difference equations and discrete orthogonal polynomials of two variables
, 2004The second order partial difference equation of two variables $ \CD u:= A_{1,1}(x) \Delta_1 \nabla_1 u + A_{1,2}(x) \Delta_1 \nabla_2 u + A_{2,1}(x) \Delta_2 \nabla_1 u + A_{2,2}(x) \Delta_2 \nabla_2 u & \qquad \qquad \qquad \qquad + B_1(x) \Delta_1 u +
Yuan Xu
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Analysis of time-varying discrete systems using discrete legendre orthogonal polynomials
Journal of the Franklin Institute, 1987A finite series expansion method using discrete Legendre orthogonal polynomials (DLOPs) is applied to analyze linear time-varying discrete systems. An effective algorithm is derived to establish a representation which relates to DLOP coefficient vector of a product function to those of its two-component functions.
Hwang, Chyi, Shyu, Kuo-Kai
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Orthogonal Polynomials and a Discrete Boundary Value Problem II
SIAM Journal on Mathematical Analysis, 1992The present paper is a continuation of an earlier work (see the paper reviewed above). The monotonicity condition of the sequence \(\{\beta_ n\}\) is given up. The result is applied to the measures \(d\mu(x)=(1-x^ 2)^ \alpha| x|^{2\beta+1}dx\) and \(d\mu(x)=| x|^{2\alpha+1} e^{-x^ 2}dx\), \(\alpha,\beta>-1\).
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Characterizations of discrete classical orthogonal polynomials
1995Summary: We give a simple unified proof of various characterizations of discrete classical orthogonal polynomials including two new ones.
Kwon K.H, Lee J. K, Yoo B.H
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