Uniform asymptotics of the Pollaczek polynomials via the Riemann–Hilbert approach

Uniform asymptotics of the Pollaczek polynomials via the Riemann–Hilbert approach

The Pollaczek weight is an example of the non-Szegö class. In this paper, we investigate the asymptotics of the Pollaczek polynomials via the Riemann–Hilbert approach. In the analysis, the original endpoints ±1 of the orthogonal interval are shifted to the Mhaskar–Rakhmanov–Saff numbers

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Veröffentlicht in:Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 2008-08, Vol.464 (2096), p.2091-2112
Hauptverfasser: Zhou, Jian-Rong, Zhao, Yu-Qiu
Format: Artikel
Sprache:eng
Schlagworte:
Airy Function
Analytic functions
Approximation
Coefficients
Hypergeometric functions
Integers
Mathematical functions
Pollaczek Polynomials
Polynomials
Riemann-Hilbert Approach
Uniform Asymptotic Expansion
Weighting functions
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Zusammenfassung:The Pollaczek weight is an example of the non-Szegö class. In this paper, we investigate the asymptotics of the Pollaczek polynomials via the Riemann–Hilbert approach. In the analysis, the original endpoints ±1 of the orthogonal interval are shifted to the Mhaskar–Rakhmanov–Saff numbers
ISSN:1364-5021
1471-2946
DOI:10.1098/rspa.2007.0385