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Approximation of analytic functions by Airy functions. (English) Zbl 1155.34002

The author solves the inhomogeneous Airy differential equation by the power series method and applies this result to estimate the error bound occuring when any analytic function is approximated by an appropriate Airy function, i.e. a solution of the homogeneous Airy differential equation.

MSC:

34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
41A30 Approximation by other special function classes
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References:

[1] Jung S.-M., Bull. Sci. Math. (2007)
[2] Jung S.-M., Abst. Appl. Anal. 2007 (2007)
[3] Kreyszig E., Advanced Engineering Mathematics, 4. ed. (1979)
[4] Lang S., Undergraduate Analysis, 2. ed. (1997) · doi:10.1007/978-1-4757-2698-5
[5] Ross C. C., Differential Equations – An Introduction with Mathematica (1995) · Zbl 0814.65072
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