Tagged: polylogarithm

Periodizing improper integrals via the partial-fraction expansion of cosecant squared reduces trigonometric-logarithmic integrals on the half-line to finite intervals.

Poisson-kernel series expansions and two-variable dilogarithm relations evaluate a difference of arctangent integrals.

The third part uses complex contours to evaluate logarithmic integrals involving inverse trigonometric functions.

The second part develops further logarithmic integral evaluations through polylogarithmic identities.

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

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

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