International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 3, Pages 541-548

On the asymptotic series solution of some higher order linear differential equations at turning points

Arthur D. Gorman

Department of Engineering Science, Lafayette College, Easton 18042, Pennsylvania, USA

Received 29 June 1983

Copyright © 1984 Arthur D. Gorman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The Lagrange manifold (WKB) formalism enables the determination of the asymptotic series solution of second-order “wave type” differential equations at turning points. The formalism also applies to higher order linear differential equations, as we make explicit here illustrating with some 4th order equations of physical significance.