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complex Liouville-Green; WKB; asymptotic approximations
We propose a variant of the classical Liouville-Green approximation theorem for linear complex differential equations of the second order. We obtain rigorous error bounds for the asymptotics at infinity, in the spirit of F. W. J. Olver’s formulation, by using rather arbitrary $\xi $-progressive paths. This approach can provide higher flexibility in practical applications of the method.
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