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CONNECTION TO CLASSICAL ORTHOGONAL POLYNOMIALS
"... Menke points on the real line and their connection to classical orthogonal polynomials ..."
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Menke points on the real line and their connection to classical orthogonal polynomials
Moments of classical orthogonal polynomials
"... The aim of this work is to find simple formulas for the moments µn for all families of classical orthogonal polynomials listed in the book by Koekoek, Lesky and Swarttouw [30]. The generating functions or exponential generating functions for those moments are given. ..."
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The aim of this work is to find simple formulas for the moments µn for all families of classical orthogonal polynomials listed in the book by Koekoek, Lesky and Swarttouw [30]. The generating functions or exponential generating functions for those moments are given.
The Associated Classical Orthogonal Polynomials
"... The associated orthogonal polynomials {pn(x; c)} are defined by the 3term recurrence relation with coefficients An, Bn, Cn for {pn(x)} with c = 0, replaced by An+c, Bn+c and Cn+c, c being the association parameter. Starting with examples where such polynomials occur in a natural way some of the we ..."
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of the wellknown theories of how to determine their measures of orthogonality are discussed. The highest level of the family of classical orthogonal polynomials, namely, the associated AskeyWilson polynomials which were studied at length by Ismail and Rahman in 1991 is reviewed with special reference
Characterizations of classical orthogonal polynomials
 Results in Math
, 1993
"... ABSTRACT. We reconsider the problem of classifying all classical orthogonal polynomial sequences which are solutions to a secondorder differential equation of the form ‘2.x/y00.x/C ‘1.x/y0.x / D n y.x/: We first obtain new (algebraic) necessary and sufficient conditions on the coefficients ‘1.x / ..."
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Cited by 12 (7 self)
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ABSTRACT. We reconsider the problem of classifying all classical orthogonal polynomial sequences which are solutions to a secondorder differential equation of the form ‘2.x/y00.x/C ‘1.x/y0.x / D n y.x/: We first obtain new (algebraic) necessary and sufficient conditions on the coefficients ‘1.x
Algorithms for Classical Orthogonal Polynomials
, 1996
"... In this article explicit formulas for the recurrence equation pn+1 (x) = (An x +Bn ) pn (x) \Gamma Cn pn\Gamma1 (x) and the derivative rules oe(x) p 0 n (x) = ff n pn+1 (x) + fi n pn (x) + fl n pn\Gamma1 (x) and oe(x) p 0 n (x) = (~ff n x + ~ fi n ) pn (x) + ~ fl n pn\Gamma1 (x) respectively ..."
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Cited by 8 (4 self)
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of classical orthogonal polynomials, and returns the corresponding data (density function,...
Classical orthogonal polynomials: dependence of parameters
, 2000
"... Most of the classical orthogonal polynomials (continuous, discrete and their qanalogues) can be considered as functions of several parameters ci. A systematic study of the variation, infinitesimal and finite, of these polynomials Pn(x; ci) with respect to the parameters ci is proposed. A method to ..."
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Cited by 4 (0 self)
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Most of the classical orthogonal polynomials (continuous, discrete and their qanalogues) can be considered as functions of several parameters ci. A systematic study of the variation, infinitesimal and finite, of these polynomials Pn(x; ci) with respect to the parameters ci is proposed. A method
A Note on Semiclassical Orthogonal Polynomials
 Bull. Belg. Math. Soc
, 1996
"... We prove that one characterization for the classical orthogonal polynomials sequences (Hermite, Laguerre, Jacobi and Bessel) cannot be extended to the semiclassical ones. 1 ..."
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Cited by 2 (2 self)
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We prove that one characterization for the classical orthogonal polynomials sequences (Hermite, Laguerre, Jacobi and Bessel) cannot be extended to the semiclassical ones. 1
THE COMPLEMENTARY POLYNOMIALS AND THE RODRIGUES OPERATOR OF CLASSICAL ORTHOGONAL POLYNOMIALS
, 2012
"... From the Rodrigues representation of polynomial eigenfunctions of a second order linear hypergeometrictype differential (difference or qdifference) operator, complementary polynomials for classical orthogonal polynomials are constructed using a straightforward method. Thus a generating function in ..."
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From the Rodrigues representation of polynomial eigenfunctions of a second order linear hypergeometrictype differential (difference or qdifference) operator, complementary polynomials for classical orthogonal polynomials are constructed using a straightforward method. Thus a generating function
LEVERRIERFADEEV ALGORITHM AND CLASSICAL ORTHOGONAL POLYNOMIALS
"... polinomio caracteŕıstico de una matriz cuadrada de elementos complejos. Palabras clave: Polinomio caracteŕıstico, funciones de transferencia, polinomios ortogonales, funcionales lineales clásicos. Using structural properties of classical orthogonal polynomials (Hermite, Laguerre, Jacobi, and Be ..."
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Cited by 1 (1 self)
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polinomio caracteŕıstico de una matriz cuadrada de elementos complejos. Palabras clave: Polinomio caracteŕıstico, funciones de transferencia, polinomios ortogonales, funcionales lineales clásicos. Using structural properties of classical orthogonal polynomials (Hermite, Laguerre, Jaco
A distributional study of discrete classical orthogonal polynomials
 J. Comput. Appl. Math
, 1995
"... For the sequences of discrete classical orthogonal polynomials (Charlier, Meixner, Hahn) we can find a functional u, which satisfies the difference distributional equation A(~bu) = flu where q ~ and ~, are polynomials ofdegrees ~< 2 and 1 respectively. From this it follows that these polynomials ..."
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Cited by 19 (3 self)
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For the sequences of discrete classical orthogonal polynomials (Charlier, Meixner, Hahn) we can find a functional u, which satisfies the difference distributional equation A(~bu) = flu where q ~ and ~, are polynomials ofdegrees ~< 2 and 1 respectively. From this it follows
Results 1  10
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