Asymptotic ExpansionsOriginally 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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Amer analytic functions apply approximations assume asymptotic expansion asymptotic forms asymptotic power series asymptotic sequence asymptotic series Bessel functions bounded bounded function c₂ calculus CALIFORN chapter Clothbound coefficients complex variable computed by formal constant continuously differentiable convergent Copson determines discussion exists extended finite number follows formal solutions formulas fundamental system hence Index infinite series interval Introduction irregular singularity Laplace's method Math mathematical method of steepest neighborhood obtain order relations Paperbound parameters partial differential equations path of integration physics Poincaré possesses an asymptotic power series expansion problems proof prove ptotic real variable result S₂ satisfies scientific sector steepest descents steepest paths substitution theorem theory tion twice continuously differentiable uniformly in arg van der Corput Volterra integral equations Y₂ zero