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Asymptotic Forms of Hermite Polynomials

Skovgaard, H. (1959) Asymptotic Forms of Hermite Polynomials. California Institute of Technology , Pasadena, CA.

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The asymptotic behavior of Hermite polynomials, H_n, (z), as n → ∞ has been investigated by several authors. The results previous to 1939, among which probably the best known are those of Plancherel and Rotach [8], are summarized in G. Szegö: Orthogonal Polynomials [10]. Some of the newer results are due to J. C. P. Miller [7], L. O. Heflinger [4] and M. Wyman. Since Hermite polynomials are special parabolic cylinder functions, attention should also be called to the results obtained in the complex plane by A. Erdélyi, M. Kennedy and J. L. McGregor [2] and by N. D. Kazarinoff [5].

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Additional Information:Prepared under contract Nonr-220(11), for the Office of Naval Research. Reference no. NR 043-121.
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ID Code:29907
Deposited By: Tony Diaz
Deposited On:18 Jun 2012 21:31
Last Modified:26 Dec 2012 15:00

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