A formal asymptotic procedure, for large $\lambda $, is developed to construct a uniform approximation to solutions of $y'' + \lambda ^2 p( {x,\lambda } )y = 0,x \in ( {a,b} )$, in regions containing finitely many zeros of $p( {x,\lambda } )$ of finite orders. The procedure used is that of constructing a simpler related equation which retains the local turning point properties of the original one.

Communications on Pure and Applied MathematicsVolume 29, Issue 4 p. 343-367 Article Uniform asymptotic solutiion for a linear ordinary differential equation with one μ-th order turning point: Analytic theory B. Willner, B. Willner Rensselaer Polytechnic InstituteSearch for more papers by this authorL. A. Rubenfeld, L. A. Rubenfeld Rensselaer Polytechnic InstituteSearch for more papers by this author B. Willner, B. Willner Rensselaer Polytechnic InstituteSearch for more papers by this authorL. A. Rubenfeld, L. A. Rubenfeld Rensselaer Polytechnic InstituteSearch for more papers by this author First published: July 1976 https://doi.org/10.1002/cpa.3160290402Citations: 6AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Citing Literature Volume29, Issue4July 1976Pages 343-367 RelatedInformation