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Resurgence relation and global asymptotic analysis of orthogonal polynomials via the Riemann-Hilbert approach

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Abstract

A global asymptotic analysis of orthogonal polynomials via the Riemann-Hilbert approach is presented, with respect to the polynomial degree. The domains of uniformity are described in certain phase variables. A resurgence relation within the sequence of Riemann-Hilbert problems is observed in the procedure of derivation. Global asymptotic approximations are obtained in terms of the Airy function. The system of Hermite polynomials is used as an illustration.

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  1. Department of Mathematics, ZhongShan University (Sun Yat-sen University), Guangzhou, 510275, China

    ShuaiXia Xu & YuQiu Zhao

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  1. ShuaiXia Xu
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  2. YuQiu Zhao
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Correspondence to YuQiu Zhao.

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Xu, S., Zhao, Y. Resurgence relation and global asymptotic analysis of orthogonal polynomials via the Riemann-Hilbert approach. Sci. China Math. 54, 661–679 (2011). https://doi.org/10.1007/s11425-010-4151-z

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  • DOI: https://doi.org/10.1007/s11425-010-4151-z

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