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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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]**E. HILLE, "Contributions to the theory of Hermitian series,"*Duke Math. J.*, v. 5, 1939, pp. 875-936. MR 1, pp. 141-142, MF 827. MR**0000870 (1:141e)****[4]**E. HILLE, "Contributions to the theory of Hermitian series. II. The representation problem,"*Trans. Amer. Math. Soc.*, v. 47, 1940, pp. 80-94. MR 1, 142. MR**0000871 (1:142a)****[5]**E. HILLE, "A class of differential operators of infinite order. I."*Duke Math. J.*, v. 7, 1940, pp. 458-495. MR 2, 184. MR**0003228 (2:184a)****[6]**E. HILLE, "Sur les fonctions analytiques définies par des séries d'Hermite,"*J. Math. Pures Appl.*, v. 40, 1961, pp. 335-342. MR**0143884 (26:1434)****[7]**E. C. TITCHMARSH,*The Theory of Functions*, Oxford Univ. Press, London, 1939.**[8]**R. ASKEY & S. WAINGER, "Mean convergence of expansions in Laguerre and Hermite series,"*Amer. J. Math.*, v. 87, 1965, pp. 695-708. MR**0182834 (32:316)**

Retrieve articles in *Mathematics of Computation*
with MSC:
42C10

Retrieve articles in all journals with MSC: 42C10

Additional Information

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

Keywords:
Hermite function series

Article copyright:
© Copyright 1980
American Mathematical Society