Titlebook: Asymptotic Analysis; J. D. Murray Textbook 1984 Springer Science+Business Media New York 1984 Approximation.Asymptotische Darstellung.Diff

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Method of steepest descents,od originated with Riemann†. It was developed in its present form independently by Debye ‡. Various extensions and rigorous proofs of some of the procedures have been given since their work and some of these are in the books cited. The basic idea and method which still has the widest applicability,

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Differential equations,ecific differential equations: the Bessel function is an example. In the case of functions defined as the solutions of differential equations which cannot be solved explicitly, these integral methods described above naturally cannot be used. (We group in the class of explicit solutions those given i

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