Resurgence relation and global asymptotic analysis of orthogonal polynomials via the Riemann-Hilbert approach
2011
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.
Keywords:
- Orthogonal polynomials
- Askey–Wilson polynomials
- Mathematical analysis
- Classical orthogonal polynomials
- Mehler–Heine formula
- Jacobi polynomials
- Koornwinder polynomials
- Discrete mathematics
- Discrete orthogonal polynomials
- Difference polynomials
- Mathematics
- Gegenbauer polynomials
- Hermite polynomials
- Wilson polynomials
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