A general method for deriving some semi-classical properties of perturbed second degree forms: the case of the Chebyshev form of second kind

DOI10.1016/j.cam.2015.10.016zbMath1343.33005OpenAlexW2218655645MaRDI QIDQ898989

Zélia da Rocha

Publication date: 21 December 2015

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2015.10.016

zbMATH Keywords

orthogonal polynomialssemi-classical formsChebyshev form of second kindperturbed formssecond-degree forms

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Computation of special functions and constants, construction of tables (65D20) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Numerical approximation and evaluation of special functions (33F05) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Related Items (3)

On connection coefficients of some perturbed of arbitrary order of the Chebyshev polynomials of second kind ⋮ Symbolic approach to the general quadratic polynomial decomposition ⋮ Common points between perturbed Chebyshev polynomials of second kind

Uses Software

• Mathematica
• na15
• OPQ

Cites Work

• On orthogonal polynomials with perturbed recurrence relations
• On co-polynomials on the real line
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• On co-recursive orthogonal polynomials and their application to potential scattering
• On mean convergence of extended Lagrange interpolation
• Finite perturbations of orthogonal polynomials
• Fourth-order differential equation for the co-modified of semi-classical orthogonal polynomials
• Variations around classical orthogonal polynomials. Connected problems
• Rational spectral transformations and orthogonal polynomials
• Second degree classical forms
• Factorization of fourth-order differential equations for perturbed classical orthogonal polynomials.
• Shohat-Favard and Chebyshev's methods in \(d\)-orthogonality
• Perturbation of the coefficients in the recurrence relation of a class of polynomials
• A large family of semi-classical polynomials: The perturbed Chebyshev
• An introduction to second degree forms
• Fourth-order differential equations satisfied by the generalized co- recursive of all classical orthogonal polynomials. A study of their distribution of zeros
• Some semi-classical and Laguerre-Hahn forms defined by pseudo-functions
• Accelerated Landweber methods based on co-dilated orthogonal polynomials
• The second-order self-associated orthogonal sequences
• Some perturbed sequences of order one of the Chebyshev polynomials of second kind
• On Co-Recursive Orthogonal Polynomials
• Some Results on Co-Recursive Associated Laguerre and Jacobi Polynomials
• Symmetric laguerre-hahn forms of classs=1
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