Tagged: infinite-series

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

Continue the study of theta functions with infinite products and connections to elliptic integrals.

Generating functions for squared harmonic numbers provide evaluations of Euler sums and logarithmic integrals.

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

An alternating Euler sum leads to harmonic-number generating functions, logarithmic integrals, and polylogarithms.

Use Ramanujan's master theorem to connect power-series coefficients with Mellin transforms of Bessel functions.

From the defining recursion for Bernoulli polynomials to their Fourier expansions and an associated integral.