Mathematical Methods in the Physical Sciences · Problem 11.25

FUNCTIONS OF A COMPLEX VARIABLE — Mary Boas

Mathematics — Methods · contour-integration-verify-formula

Problem

Verify the formula by contour integration or as indicated. Assume a>0a > 0, m>0m > 0. PV∫0∞cos⁡mx dxx2−a2=−π2asin⁡maPV\int_0^\infty \frac{\cos mx\,dx}{x^2-a^2} = -\frac{\pi}{2a}\sin ma

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