The rate of convergence of Hermite function series
نویسندگان
چکیده
منابع مشابه
The Rate of Convergence of Hermite Function Series
Let a > 0 be the least upper bound of y for which f(z) 0(e-°My) for some positive constant q as |z| -+ o» on the real axis. It is then proved that at least an infinite subsequence of the coefficients \an} in oo f(z) = e-z2/2 £ anHn(z), n=0 where the Hn are the normalized Hermite polynomials, must satisfy certain lower bounds. The theorems show two striking facts. First, the convergence rate of ...
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15 صفحه اولAsymptotic Coefficients of Hermite Function Series
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 He...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1980
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1980-0583508-3