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The rate of convergence of Hermite function series. (English) Zbl 0459.40005

MSC:
40A05 Convergence and divergence of series and sequences
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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References:
[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. · Zbl 0022.36501
[4] Einar Hille, Contributions to the theory of Hermitian series. II. The representation problem, Trans. Amer. Math. Soc. 47 (1940), 80 – 94. · Zbl 0022.36502
[5] Einar Hille, A class of differential operators of infinite order, I, Duke Math. J. 7 (1940), 458 – 495. · Zbl 0025.25702
[6] Einar Hille, Sur les fonctions analytiques définies par des séries d’Hermite., J. Math. Pures Appl. (9) 40 (1961), 335 – 342 (French). · Zbl 0100.06704
[7] E. C. TITCHMARSH, The Theory of Functions, Oxford Univ. Press, London, 1939. · Zbl 0022.14602
[8] Richard Askey and Stephen Wainger, Mean convergence of expansions in Laguerre and Hermite series, Amer. J. Math. 87 (1965), 695 – 708. · Zbl 0125.31301
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