By R. B. Paris

the writer describes the lately constructed idea of Hadamard expansions utilized to the high-precision (hyperasymptotic) overview of Laplace and Laplace-type integrals. This fresh technique builds at the recognized asymptotic approach to steepest descents, of which the hole bankruptcy offers a close account illustrated via a sequence of examples of accelerating complexity. A dialogue of uniformity difficulties linked to a number of coalescence phenomena, the Stokes phenomenon and hyperasymptotics of Laplace-type integrals follows. the rest chapters take care of the Hadamard enlargement of Laplace integrals, with and with out saddle issues. difficulties of alternative varieties of saddle coalescence also are mentioned. The textual content is illustrated with many numerical examples, which support the reader to appreciate the extent of accuracy achieveable. the writer additionally considers functions to a few very important precise capabilities. This ebook is perfect for graduate scholars and researchers operating in asymptotics.

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