A two-parameter family of orthogonal polynomials with respect to a Jacobi-type weight on the unit circle

Christer Glader

doi:10.1006/jmaa.1999.6621

A two-parameter family of orthogonal polynomials with respect to a Jacobi-type weight on the unit circle

Christer Glader^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › Scientific › peer-review

6 Citations (Scopus)

Abstract

A two-parameter family of polynomials is introduced by a recursion formula. The polynomials are orthogonal on the unit circle with respect to the weight ω_α,β(θ)=(1-z)^α(1+z) ^β2, α,β-12, z=e^iθ. Explicit representation, norm estimates, shift identities, and explicit connection to Jacobi polynomials on the real interval [-1,1] is presented.

Original language	English
Pages (from-to)	583-599
Number of pages	17
Journal	Journal of Mathematical Analysis and Applications
Volume	240
Issue number	2
DOIs	https://doi.org/10.1006/jmaa.1999.6621
Publication status	Published - 15 Dec 1999
MoE publication type	A1 Journal article-refereed

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title = "A two-parameter family of orthogonal polynomials with respect to a Jacobi-type weight on the unit circle",

abstract = "A two-parameter family of polynomials is introduced by a recursion formula. The polynomials are orthogonal on the unit circle with respect to the weight ωα,β(θ)=(1-z)α(1+z) β2, α,β-12, z=eiθ. Explicit representation, norm estimates, shift identities, and explicit connection to Jacobi polynomials on the real interval [-1,1] is presented.",

author = "Christer Glader",

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AU - Glader, Christer

PY - 1999/12/15

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N2 - A two-parameter family of polynomials is introduced by a recursion formula. The polynomials are orthogonal on the unit circle with respect to the weight ωα,β(θ)=(1-z)α(1+z) β2, α,β-12, z=eiθ. Explicit representation, norm estimates, shift identities, and explicit connection to Jacobi polynomials on the real interval [-1,1] is presented.

AB - A two-parameter family of polynomials is introduced by a recursion formula. The polynomials are orthogonal on the unit circle with respect to the weight ωα,β(θ)=(1-z)α(1+z) β2, α,β-12, z=eiθ. Explicit representation, norm estimates, shift identities, and explicit connection to Jacobi polynomials on the real interval [-1,1] is presented.

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U2 - 10.1006/jmaa.1999.6621

DO - 10.1006/jmaa.1999.6621

M3 - Article

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SN - 0022-247X

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EP - 599

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

A two-parameter family of orthogonal polynomials with respect to a Jacobi-type weight on the unit circle

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