Mathematical Methods in the Physical Sciences · Problem 11.27

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 > 0

m > 0

PV\int_0^\infty \frac{x\sin mx\,dx}{x^2-a^2} = \frac{\pi}{2}\cos ma

Hint for Problems 26 and 27: Differentiate Problems 24 and 25 with respect to

m