References
R.Askey and S.Wainger: “Mean convergence of expansions in Laguerre- and Hermite-series”, Am. Journ. of math., 87, 1965.
K.Chandrasekharan: “Classical Fourier Transforms”, Berlin, 1989.
A.Erdélyi: “Asymptotic solutions of differential equations with transition points or singularities”, Journ. of math. phys., Vol.1, Nr.1, 1960.
A.Erdélyi et al.: “Higher transcendental functions”, New York, 1953.
M. Grawe: “Asymptotik der Hermite’schen Orthonormalfunktionen und ihre Anwendung auf das Wachstum von Hermite-Reihen”, Diplomarbeit, Bonn, 1996.
H. and B. Jeffreys: “Methods of mathematical physics”, Cambridge, 1956.
N.N.Lebedew: “Spezielle Funktionen und ihre Anwendung”, Zürich, 1973.
C.Markett: “Norm estimates for (C,δ) means of Hermite expansions”, Acta Math. Hung. 43 (3–4), 1984.
A.F.Nikiforov and V.B.Uvarov: “Special functions of mathematical physics”, Basel, 1988.
G.Szegö: “Orthogonal polynomials”, New York, 1939.
E.C.Titchmarsh: “The theory of the Riemann Zeta-Function”, Oxford, 1951.
G.N.Watson: “A treatise on the theory of Bessel functions”, Cambridge, 1922.
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Grawe, M. Asymptotic Growth of Hermite Series and an Application to the Theory of the Riemann Zeta Function. Results. Math. 31, 105–114 (1997). https://doi.org/10.1007/BF03322153
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DOI: https://doi.org/10.1007/BF03322153