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."

arXiv commentChanged 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

Cited by in corpus (2)

• On an integral involving the digamma function
• Some applications of the Dirichlet integrals to the summation of series and the evaluation of integrals involving the Riemann zeta function