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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


The rate of convergence of Hermite function series
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by John P. Boyd PDF
Math. Comp. 35 (1980), 1309-1316 Request permission


Let $\alpha > 0$ be the least upper bound of $\gamma$ for which \[ f(z) \sim O({e^{ - q|z|\gamma }})\] for some positive constant q as $|z| \to \infty$ on the real axis. It is then proved that at least an infinite subsequence of the coefficients $\{ {a_n}\}$ in \[ f(z) = {e^{ - {z^2}/2}}\sum \limits _{n = 0}^\infty {{a_n}{H_n}(z),} \] where the ${H_n}$ 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 $\rho$ for an entire function or the location of the nearest singularity for a singular function as for a power series but also upon $\alpha$, 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 $f(z)$ and $\exp (-1/2 z^2)$ the poorer the convergence of the Hermite series will be.
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Math. Comp. 35 (1980), 1309-1316
  • MSC: Primary 42C10
  • DOI:
  • MathSciNet review: 583508