Tagged: residue-theorem

Integrating a complex power around a keyhole cut along the negative real axis evaluates a rational integral involving the sine of a logarithm.

Residue calculus on a rectangular contour shows that the hyperbolic secant is its own Fourier transform up to scaling.

Integrating a meromorphic function around a horizontal strip of height two pi evaluates a real integral mixing exponential and rational factors.

The first part of a series on logarithmic integrals: harmonic-number sums, polylogarithms, and residues.

A contour-integral approach to an infinite trigonometric series, with an application of equidistribution.