By R. Wong

ISBN-10: 0898714974

ISBN-13: 9780898714975

I'm learning "Asyptotic Expantions" in graduate university. to review this box, this e-book is particularly vital reference one in all them.

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**Example text**

As 2 -* oo uniformly in |arg(z — c)|

66). If F(z) has a convergent expansion of the form which can be integrated term by term to give 5. Watson's Lemma 31 then the behavior as t -» 0+ would be established. 71) is not valid. 71). Converse to Watson's Lemma. 68). // as 2 -* oo uniformly in |arg(z — c)|

In order to generalize, we consider the integral 22 I Fundamental Concepts of Asymptotics where y is a fixed real number, and the path of integration is the straight line joining t — 0 to t = aoeiy. The following result is given in Wyman (1964, p. 249). Generalized Watson's Lemma. 13) exists for some fixed z = z0, and that as t -> 0 along arg t = y, where Re and Re Then as z -» oo in |arg(zelv)| < rc/2 — A, for any real number A in the interval 0 < A <: n/2. Proof. The general properties of Laplace integrals (Widder 1941, p.

### Asymptotic Approximation of Integrals (Classics in Applied Mathematics) by R. Wong

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