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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:

[1] S.-M. Jung, Legendre’s differential equation and its Hyers-Ulam stability, Abst. Appl. Anal., in press; S.-M. Jung, Legendre’s differential equation and its Hyers-Ulam stability, Abst. Appl. Anal., in press · Zbl 1153.34306
[2] Kreyszig, E., Advanced Engineering Mathematics (1979), John Wiley & Sons: John Wiley & Sons New York · Zbl 0517.00001
[3] Protter, M. H.; Morrey, C. B., A First Course in Real Analysis (1991), Springer: Springer New York · Zbl 0352.26001
[4] Ross, C. C., Differential Equations - An Introduction with Mathematica (1995), Springer: Springer New York · Zbl 0814.65072
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