Displaying similar documents to “On the Sensitivity of Orthogonal Polynomials to Perturbations in the Moments.”

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

Similarity:

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...

Classical and generalized Jacobi polynomials orthogonal with different weight functions and differential equations satisfied by these polynomials

Marčoková, Mariana, Guldan, Vladimír

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In this contribution we deal with classical Jacobi polynomials orthogonal with respect to different weight functions, their special cases - classical Legendre polynomials and generalized brothers of them. We derive expressions of generalized Legendre polynomials and generalized ultraspherical polynomials by means of classical Jacobi polynomials.

On block recursions, Askey's sieved Jacobi polynomials and two related systems

Bernarda Aldana, Jairo Charris, Oriol Mora-Valbuena (1998)

Colloquium Mathematicae

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Two systems of sieved Jacobi polynomials introduced by R. Askey are considered. Their orthogonality measures are determined via the theory of blocks of recurrence relations, circumventing any resort to properties of the Askey-Wilson polynomials. The connection with polynomial mappings is examined. Some naturally related systems are also dealt with and a simple procedure to compute their orthogonality measures is devised which seems to be applicable in many other instances.