The rate of convergence of Hermite function series
Author:
John P. Boyd
Journal:
Math. Comp. 35 (1980), 13091316
MSC:
Primary 42C10
MathSciNet review:
583508
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Abstract: Let be the least upper bound of for which for some positive constant q as on the real axis. It is then proved that at least an infinite subsequence of the coefficients in where the are the normalized Hermite polynomials, must satisfy certain lower bounds. The theorems show two striking facts. First, the convergence rate of a Hermite series depends not only upon the order for an entire function or the location of the nearest singularity for a singular function as for a power series but also upon , thus making the convergence theory of Hermitian series more complicated (and interesting) than that for any ordinary Taylor expansion. Second, the poorer the match between the asymptotic behavior of and the poorer the convergence of the Hermite series will be.
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 J. P. BOYD, "Hermite polynomial methods for obtaining analytical and numerical solutions to eigenvalue problems in unbounded and spherical geometry," J. Comput. Phys. (Submitted.)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198005835083
PII:
S 00255718(1980)05835083
Keywords:
Hermite function series
Article copyright:
© Copyright 1980
American Mathematical Society
