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Methods of Mathematical Physics, Third Edition by Bertha Jeffreys, Harold Jeffreys

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Chapter 12CONTOUR INTEGRATION AND BROMWICH’S INTEGRAL

‘Go round about, Peer Gynt!’

IBSEN, Peer Gynt

12·01. Description of method.

This method of evaluating definite integrals is based directly on Cauchy’s theorem. We have had instances of it already in the proofs of Cauchy’s inequality and Laurent’s theorem. A simple example is the following. Take

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where a and b are real and a > b > 0. The integrand is an even function of θ, and therefore

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Put

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