  We show that
  F_a(x)=\frac{\ln \Gamma (x+1)}{x\ln(ax)} is a Pick function for a\ge 1 and
find its integral representation.
  We also consider the function f(x)=(\frac{\pi^{x/2}}{\Gamma(1+x/2)})^{1/(x\ln
x)} and show that \ln f(x+1) is a Stieltjes function and that f(x+1) is
completely monotonic on (0,\infty). In particular f(n)=\Omega_n^{1/(n\ln
n)},n\ge 2 is a
  Hausdorff moment sequence. Here \Omega_n is the volume of the unit ball in
Euclidean n-space
