Jan 26, 2025
More residue calculus: sinc squared, fractional exponent, log, pie contour
[Click here for a PDF version of this post] Sinc squared. This is problem 31(g) from [1]. Find \begin{equation}\label{eqn:sincSquared:20} I = \int_{-\infty}^\infty \frac{\sin^2 x}{x^2} dx. \end{equation} We will use the same upper half plane semicircular contour, enclosing the second order pole at the origin. This time we write \begin{equation}\label{eqn:sincSquared:40} \sin^2 x = \frac{ 1 –…
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