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A Szegö Quadrature Formula Arising from q-Starlike Functions
| Content Provider | Scilit |
|---|---|
| Author | Rønning, Frode |
| Copyright Year | 2020 |
| Description | In a similar way as quadrature formulas on a real interval are constructed using zeros of orthogonal polynomials as nodes, Jones et al. [3] showed how to construct a quadrature formula based on polynomials orthogonal on the unit circle (Szegö polynomials). The Szegö polynomials have their zeros inside the unit circle, but by combining the Szegö polynomials and the reciprocal Szegö polynomials in a certain way, they obtained polynomials with zeros on the unit circle. By using these zeros as nodes, and by choosing weights in a certain manner, which will be described later, they showed that the resulting quadrature formula would have a maximal domain of validity in the set of Laurent polynomials. This type of quadrature formula is referred to as a Szegö quadrature formula. Further, there is a close connection between Szegö polynomials and Carathéodory functions Via the elements of a certain continued fraction (positive PC-fraction) as shown by Jones et al. in [2]. Now, given the connection between q-starlike functions and Carathéodory functions which will be established below, we are justified in talking about a quadrature formula arising from q-starlike functions. Book Name: Continued fractions and orthogonal functions |
| Related Links | https://content.taylorfrancis.com/books/download?dac=C2006-0-16181-4&isbn=9781003072591&format=googlePreviewPdf |
| Ending Page | 352 |
| Page Count | 8 |
| Starting Page | 345 |
| DOI | 10.1201/9781003072591-14 |
| Language | English |
| Publisher | Informa UK Limited |
| Publisher Date | 2020-12-17 |
| Access Restriction | Open |
| Subject Keyword | Book Name: Continued Fractions and Orthogonal Functions Functions Szegö Quadrature Formula Starlike Polynomials Circle |
| Content Type | Text |
| Resource Type | Chapter |
