Results 271 to 280 of about 58,842 (311)

Discrete orthogonal polynomials – polynomial modification of a classical functional

Journal of Difference Equations and Applications, 2001
Polynomial modifications of a classical discrete linear functional are examined in detail, in particular when the new linear functional remains classical. New addition formulas are deduced for Charlier, Meixner and Hahn polynomials from the Christoffei representation and results are also given for a particular generalized Meixner family.
Ronveaux, André, Salto, L.
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Extremal problems, inequalities, and classical orthogonal polynomials

Applied Mathematics and Computation, 2002
In this survey paper we give a short account on characterizations for very classical orthogonal polynomials via extremal problems and the corresponding inequalities. Besides the basic properties of the classical orthogonal polynomials, we consider polynomial inequalities of Landau and Kolmogoroff type, some weighted polynomial inequalities in \(L^2 ...
Agarwal, Ravi P., Milovanović, Gradimir V.   +1 more
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Another Characterization of the Classical Orthogonal Polynomials

SIAM Journal on Mathematical Analysis, 1972
The classical orthogonal polynomials of Jacobi, Laguerre and Hermite are characterized as the only orthogonal polynomials with a differentiation formula of the form \[ \pi (x)P'_n (x) = \left( {\alpha _n x + \beta _n } \right)P_n (x) + \gamma _n P_{n - 1} (x),\quad n \geqq 1,\] where $\pi (x)$ is a polynomial.
Al-Salam, W. A., Chihara, T. S.
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Positive Sums of the Classical Orthogonal Polynomials

SIAM Journal on Mathematical Analysis, 1977
An expansion as a sum of squares of Jacobi polynomials \(P_n^{(\alpha , \beta )}(x)\) is used to prove that if \(0 \leq \lambda \leq \alpha + \beta\) and \(\beta \geq -1/2\), then \[ \sum_{k=1}^{n} \frac{(\lambda +1)_{n-k}}{(n-k)!} \frac{(\lambda +1)_k}{k!} \frac{P_k^{(\alpha ,\beta )}(x)}{P_k^{(\alpha ,\beta )}} = 0,\quad -1\leq x \leq \infty, \tag{\(*
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Classical Appell's Orthogonal Polynomials

2022
P.K. Suetin, E.V. Pankratiev
openaire   +1 more source

Spectral Solutions for Differential and Integral Equations with Varying Coefficients Using Classical Orthogonal Polynomials

Bulletin of the Iranian Mathematical Society, 2018
E. H. Doha, Youssri Hassan Youssri, M. A. Zaky   +2 more
semanticscholar   +1 more source

Click and Bio-Orthogonal Reactions with Mesoionic Compounds

Chemical Reviews, 2021
Margaux Riomet, Carlotta Figliola, Davide Audisio   +2 more
exaly  

Characterizations of the Symmetric $$T_{(\theta , q)}$$-Classical Orthogonal q-Polynomials

Mediterranean Journal of Mathematics, 2022
B. Bouras, Y. Habbachi, F. Marcellán
semanticscholar   +1 more source

Classification of classical orthogonal polynomials

1997
The authors consider the differential equation \[ l_2(x)y''+ l_1(x)y'= \lambda_n y(x), \tag{\(*\)} \] , where \(x\in R\), \(l_1(x)= l_{11}x+ l_{10}\) and \(l_2(x)= l_{22}x^2+ l_{21}x+ l_{20}\) with certain coefficients \(l_{ij}\) while \(\lambda_n= n(n-1)l_{22}+ nl_{11}\) \((n\geq 0)\), and discuss different cases for which \((*)\) has polynomial ...
KIL H. KWON, Lance L. Littlejohn
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Fabrication of Biomedical Scaffolds Using Biodegradable Polymers

Chemical Reviews, 2021
Alina Kirillova, Darya Asheghali, Sophia Dort   +2 more
exaly