M. Vianello, Dipartimento di Matematica Pura e Applicata, Universita di Padova, Via Belzoni 7, 35131 Padova, ITALY
E-mail: spigler@dmsa.unipd.it, marcov@math.unipd.it
Abstract. We propose a variant of the classical Liouville-Green approximation theorem for linear {\em complex\/} differential equations of the second order. We obtain rigorous error bounds for the asymptotics {\em 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.
AMSclassification. 34E20, 34M60
Keywords. Complex Liouville-Green, WKB, asymptotic approximations