Displaying similar documents to “Orthogonal polynomials related to the oscillatory-chebyshev weight function”

An extension of typically-real functions and associated orthogonal polynomials

Iwona Naraniecka, Jan Szynal, Anna Tatarczak (2011)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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Two-parameters extension of the family of typically-real functions is studied. The definition is obtained by the Stjeltjes integral formula. The kernel function in this definition serves as a generating function for some family of orthogonal polynomials generalizing Chebyshev polynomials of the second kind. The results of this paper concern the exact region of local univalence, bounds for the radius of univalence, the coefficient problems within the considered family as well as the basic...

An extension of typically-real functions and associated orthogonal polynomials

Iwona Naraniecka, Jan Szynal, Anna Tatarczak (2011)

Annales UMCS, Mathematica

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Two-parameters extension of the family of typically-real functions is studied. The definition is obtained by the Stjeltjes integral formula. The kernel function in this definition serves as a generating function for some family of orthogonal polynomials generalizing Chebyshev polynomials of the second kind. The results of this paper concern the exact region of local univalence, bounds for the radius of univalence, the coefficient problems within the considered family as well as the basic...

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D. Mangeron, A. M. Krall, D. L. Fernández (1983)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

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Special Classes of Orthogonal Polynomials and Corresponding Quadratures of Gaussian Type

Milovanovic, Gradimir V., Cvetkovic, Aleksandar S. (2012)

Mathematica Balkanica New Series

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MSC 2010: 33C47, 42C05, 41A55, 65D30, 65D32 In the first part of this survey paper we present a short account on some important properties of orthogonal polynomials on the real line, including computational methods for constructing coefficients in the fundamental three-term recurrence relation for orthogonal polynomials, and mention some basic facts on Gaussian quadrature rules. In the second part we discuss our Mathematica package Orthogonal Polynomials (see [2]) and show...