Bender, Carl M.; Orszag, Steven A. Advanced mathematical methods for scientists and engineers. (English) Zbl 0417.34001 International Series in Pure and Applied Mathematics. New York etc.: McGraw-Hill Book Company XIV, 593 p. DM 74.10 (1978). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 5 ReviewsCited in 869 Documents MSC: 34-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordinary differential equations 34A45 Theoretical approximation of solutions to ordinary differential equations 34E05 Asymptotic expansions of solutions to ordinary differential equations 41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.) 34E20 Singular perturbations, turning point theory, WKB methods for ordinary differential equations 40E05 Tauberian theorems Keywords:approximate analytical solutions to differential and difference equations; asymptotic series theory; asymptotic expansions of integrals; algebraic and differential equations; eigenvalue problems; singular perturbations; summation of series; Wkb approximation PDFBibTeX XML Digital Library of Mathematical Functions: §32.11(i) First Painlevé Equation ‣ §32.11 Asymptotic Approximations for Real Variables ‣ Properties ‣ Chapter 32 Painlevé Transcendents