A q-integral representation of Rogers' q-ultraspherical polynomials and some applications (Q1071914)
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scientific article; zbMATH DE number 3939728
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A q-integral representation of Rogers' q-ultraspherical polynomials and some applications |
scientific article; zbMATH DE number 3939728 |
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A q-integral representation of Rogers' q-ultraspherical polynomials and some applications (English)
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1986
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The continuous q-ultraspherical polynomials of Rogers are turning out to be richer than one could have expected. An extension of Szegö's series expansion for ultraspherical polynomials is shown here to be equivalent to a q-integral representation of these polynomials. From this the authors derive a simple proof of the Gasper-Rahman formula for the Poisson kernel, and a very attractive asymptotic expansion for these polynomials on the spectral interval.
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q-ultraspherical polynomials of Rogers
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Gasper-Rahman formula
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Poisson kernel
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0.9366065
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0.93033564
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0.91064847
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0.9073296
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0.9025836
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0.89134824
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0.8901596
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