The rate of convergence of Hermite function series

Author:
John P. Boyd

Journal:
Math. Comp. **35** (1980), 1309-1316

MSC:
Primary 42C10

DOI:
https://doi.org/10.1090/S0025-5718-1980-0583508-3

MathSciNet review:
583508

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Abstract: Let be the least upper bound of for which

*q*as on the real axis. It is then proved that at least an infinite subsequence of the coefficients in

**[1]**M. ABRAMOWITZ & I. A. STEGUN, Eds.,*Handbook of Mathematical Functions*, Dover, New York, 1965. MR 29 #4914.**[2]**J. P. BOYD, "Hermite polynomial methods for obtaining analytical and numerical solutions to eigenvalue problems in unbounded and spherical geometry,"*J. Comput. Phys*. (Submitted.)**[3]**Einar Hille,*Contributions to the theory of Hermitian series*, Duke Math. J.**5**(1939), 875–936. MR**0000870****[4]**Einar Hille,*Contributions to the theory of Hermitian series. II. The representation problem*, Trans. Amer. Math. Soc.**47**(1940), 80–94. MR**0000871**, https://doi.org/10.1090/S0002-9947-1940-0000871-3**[5]**Einar Hille,*A class of differential operators of infinite order, I*, Duke Math. J.**7**(1940), 458–495. MR**0003228****[6]**Einar Hille,*Sur les fonctions analytiques définies par des séries d’Hermite.*, J. Math. Pures Appl. (9)**40**(1961), 335–342 (French). MR**0143884****[7]**E. C. TITCHMARSH,*The Theory of Functions*, Oxford Univ. Press, London, 1939.**[8]**Richard Askey and Stephen Wainger,*Mean convergence of expansions in Laguerre and Hermite series*, Amer. J. Math.**87**(1965), 695–708. MR**0182834**, https://doi.org/10.2307/2373069

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DOI:
https://doi.org/10.1090/S0025-5718-1980-0583508-3

Keywords:
Hermite function series

Article copyright:
© Copyright 1980
American Mathematical Society