Geodesic
A variant of the complex Liouville-Green approximation theorem
Archivum mathematicum, Tome 36 (2000) no. 3, pp. 213-218 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 34E20, 34M35, 34M60
Keywords: complex Liouville-Green; WKB; asymptotic approximations 
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     author = {Spigler, Renato and Vianello, Marco},
     title = {A variant of the complex {Liouville-Green} approximation theorem},
     journal = {Archivum mathematicum},
     pages = {213--218},
     year = {2000},
     volume = {36},
     number = {3},
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     zbl = {1058.34128},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2000_36_3_a6/}
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Spigler, Renato; Vianello, Marco. A variant of the complex Liouville-Green approximation theorem. Archivum mathematicum, Tome 36 (2000) no. 3, pp. 213-218. http://geodesic.mathdoc.fr/item/ARM_2000_36_3_a6/