Title: Generalized Stieltjes constants and integrals involving the log-log function: Kummer's Theorem in action,
Abstract: In this note, we recall Kummer's Fourier series expansion of the 1-periodic
function that coincides with the logarithm of the Gamma function on the unit
interval $(0,1)$, and we use it to find closed forms for some numerical series
related to the generalized Stieltjes constants, and some integrals involving
the function $x\mapsto \ln \ln(1/x)$.