Resurgence relation and global asymptotic analysis of orthogonal polynomials via the Riemann-Hilbert approach (Q547396)
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scientific article; zbMATH DE number 5916812
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Resurgence relation and global asymptotic analysis of orthogonal polynomials via the Riemann-Hilbert approach |
scientific article; zbMATH DE number 5916812 |
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Resurgence relation and global asymptotic analysis of orthogonal polynomials via the Riemann-Hilbert approach (English)
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1 July 2011
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The authors present a global asymptotic analysis of orthogonal polynomials for large degree by means of the well known Riemann-Hilbert approach. The authors compute the exact domains of validity of the approximation and find a resurgence relation within the sequence of Riemann-Hilbert problems involved in the derivation. Global asymptotic approximations are given in terms of Airy functions. The authors illustrate their approach by means of Hermite polynomials.
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Riemann-Hilbert approach
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resurgence relation
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uniform asymptotics
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orthogonal polynomials
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Hermite polynomials
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Airy function
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