Double Integrals for Euler's Constant and ln(4/Pi) and an Analog of Hadjicostas's Formula
Classical Analysis and ODEs
2009-09-29 v3 General Mathematics
Number Theory
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."
Keywords
Cite
@article{arxiv.math/0211148,
title = {Double Integrals for Euler's Constant and ln(4/Pi) and an Analog of Hadjicostas's Formula},
author = {Jonathan Sondow},
journal= {arXiv preprint arXiv:math/0211148},
year = {2009}
}
Comments
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