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Approximation of analytic functions by Hermite functions. (English) Zbl 1186.41016
The author solves the inhomogeneous Hermite equation with a power series on the right. This is used to establish the error bound \(O(x^2)\), \(x \to 0\), for the approximation of an analytic function by a solution of the homogeneous Hermite equation.

41A30 Approximation by other special function classes
34B30 Special ordinary differential equations (Mathieu, Hill, Bessel, etc.)
34A05 Explicit solutions, first integrals of ordinary differential equations
Full Text: DOI
[1] S.-M. Jung, Legendre’s differential equation and its Hyers-Ulam stability, Abst. Appl. Anal., in press · Zbl 1153.34306
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[3] Protter, M.H.; Morrey, C.B., A first course in real analysis, (1991), Springer New York · Zbl 0352.26001
[4] Ross, C.C., Differential equations - an introduction with Mathematica, (1995), Springer New York · Zbl 0814.65072
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