Asymptotic Expansions of Integrals - download pdf or read online

By Norman Bleistein

ISBN-10: 0486650820

ISBN-13: 9780486650821

Excellent introductory textual content, written via specialists, offers a coherent and systematic view of rules and strategies. issues include integration through elements, Watson's lemma, LaPlace's procedure, desk bound part, and steepest descents. extra topics include the Mellin remodel procedure and not more common points of the strategy of steepest descents. 1975 edition.

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Sample text

Granted this, which will also be proved later, one notes that Q induces an injection Q of the space X into cm; it follows in particular that Q is light at every point of C"'. It will also be seen below that the ring P of polynomials inn variables is integral over pr, hence Q is a proper mapping. Therefore, by [44a: Corollary, p. 87], Q(X) is an analytic subset of C"', and as such is a complex analytic space, of which the underlying space is homeomorphic to X. (In this case, since only polynomials are involved, a direct, purely algebraic proof of the same fact can be given, not using the analytical results of [44a], cf.

Suppose K(z) =F 0 for every z e D. p(Z) = --_ - log K(z). ,,=o

5Yt)c'Jl. 5Yt to T 0 T Since infinitely many elements of the sequence. 5Yt. 5Yt' of b0 such that T""T0• 00 , 00 00 00 00 00 • 00 30 HOLOMORPHIC FUNCTIONS AND MAPPINGS ON A BOUNDED DOMAIN is defined and equal to the identity there. It now remains to prove that the ranges of T 0 and of T lie in D. We treat the case of T""" Let beD and let B be a compact neighborhood of b, B=BcD. The compositum T 1- 1 Tm is defined for all l and m. We claim that T 1- 1T,. converges weakly to the identity on D. We consider {T1- 1 Tm-id.

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Asymptotic Expansions of Integrals by Norman Bleistein

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