Representations of the Glaisher-Kinkelin constant deduced from integrals due to Féaux and Kummer

We present two integral representations of the logarithm of the Glaisher-Kinkelin constant. The calculations are based on definite integral expressions of $\log \mathrm{\Gamma }(x)$, $\mathrm{\Gamma }$ being the usual Gamma function, due respectively to Féaux and Kummer. The connection between the second formula and an infinite series expansion of the Glaisher-Kinkelin constant is also outlined.