Double Integrals for Euler's Constant and ln(4/Pi) and an Analog of Hadjicostas's Formula

Abstract

We give analogs for Euler's constant and ln(4/Pi) of the well-known double integrals for zeta(2) and zeta(3). We also give a series for ln(4/Pi) which reveals it to be an "alternating Euler constant."

Changed the title and added an analog for the alternating zeta function of Hadjicostas's double integral for the Riemann zeta function. A special case is an integral involving the Glaisher-Kinkelin constant