Courier Corporation, 2012年4月27日 - 128 頁
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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AN(x analytic functions approximately assume asym asymptotic behavior asymptotic expansion asymptotic forms asymptotic power series asymptotic representation asymptotic sequence asymptotic series asymptotic sum asymptotically equal Bessel functions BN(x bounded function chapter coefficients complex plane complex variable computed by formal constant continuous function continuously differentiable convergent Copson derivatives determines exists extended ﬁn finite number finite or infinite formal expansion formal solutions formula functions defined fundamental system hence hold uniformly infinite series interval irregular singularity l¢nl Laplace integrals Laplace’s method linearly independent linearly independent solutions Liouville’s Math method of steepest multiplicative asymptotic sequence neighborhood number of terms obtain order relations parameters path of integration possesses an asymptotic power series expansion prove ptotic real variable represented asymptotically result satisfies sector stationary points steepest descents steepest paths Stokes theorem in sec theory transition point twice continuously differentiable uniformly in arg van der Corput Volterra integral equations