Originally prepared for the Office of Naval Research, this important monograph introduces various methods for the asymptotic evaluation of integrals containing a large parameter, and solutions of ordinary linear differential equations by means of asymptotic expansions. Author's preface. Bibliography.
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algebra analytic functions applied approximation assume asym asymptotic behavior asymptotic expansion asymptotic forms asymptotic power series asymptotic represeatation asymptotic sequence asymptotic series Bessel functions Bibliography bounded function chapter chemistry Classic coatribution coavergeat coefficieats complex plane complex variable computed by formal constant converges Copson derivatives differeatial equation exists exponeatially extended finite number finite or infinite formal solutions formula Fourier functions defined fundamental system hence iategral iavestigated infinite series interval INTRODUCTION irregular singularity Laplace Laplace's method linearly independent Math mathematical mechanics method of steepest multiplicative asymptotic sequence neighborhood number of terms obtain parameters path of integration poiats possesses an asymptotic power series expansion problems prove ptotic quantum real axis real variable result satisfies sector stationary points steepest descents steepest paths substitution sufficieatly large theorem theory transformation twice coatinuously differeatiable uniformly in arg van der Corput Volterra integral equations zero