Asymptotic Coefficients of Hermite Function Series

@inproceedings{Boyd2003AsymptoticCO,
  title={Asymptotic Coefficients of Hermite Function Series},
  author={John P. Boyd},
  year={2003}
}
By using complex variable methods (steepest descent and residues) to asymptotically evaluate the coefftcient integrals, the numerical analysis of Hermite function series is discussed. There are striking similarities and differences with the author’s earlier work on Chebyshev polynomial methods (J. Comp. Phys. 45 (1982), 45-49) for infinite or semi-infinite domains. Like Chebyshev series, the Hermite coefficients are asymptotically given by the sum of two types of terms: (i) stationary point… CONTINUE READING
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