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

Bernarda Aldana; Jairo Charris; Oriol Mora-Valbuena

Colloquium Mathematicae (1998)

  • Volume: 78, Issue: 1, page 57-91
  • ISSN: 0010-1354

Abstract

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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.

How to cite

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Aldana, Bernarda, Charris, Jairo, and Mora-Valbuena, Oriol. "On block recursions, Askey's sieved Jacobi polynomials and two related systems." Colloquium Mathematicae 78.1 (1998): 57-91. <http://eudml.org/doc/210606>.

@article{Aldana1998,
abstract = {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.},
author = {Aldana, Bernarda, Charris, Jairo, Mora-Valbuena, Oriol},
journal = {Colloquium Mathematicae},
keywords = {continued fractions; moment functionals; Askey-Wilson and Rogers polynomials; Chebyshev; sieved orthogonal polynomials; orthogonal polynomials; Jacobi and ultraspherical polynomials; Askey-Wilson polynomials; orthogonality measures},
language = {eng},
number = {1},
pages = {57-91},
title = {On block recursions, Askey's sieved Jacobi polynomials and two related systems},
url = {http://eudml.org/doc/210606},
volume = {78},
year = {1998},
}

TY - JOUR
AU - Aldana, Bernarda
AU - Charris, Jairo
AU - Mora-Valbuena, Oriol
TI - On block recursions, Askey's sieved Jacobi polynomials and two related systems
JO - Colloquium Mathematicae
PY - 1998
VL - 78
IS - 1
SP - 57
EP - 91
AB - 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.
LA - eng
KW - continued fractions; moment functionals; Askey-Wilson and Rogers polynomials; Chebyshev; sieved orthogonal polynomials; orthogonal polynomials; Jacobi and ultraspherical polynomials; Askey-Wilson polynomials; orthogonality measures
UR - http://eudml.org/doc/210606
ER -

References

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