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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.

MSC:
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
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References:
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