A Pick function related to the sequence of volumes of the unit ball in n-space

Christian Berg, Henrik L. Pedersen

We show that F_a(x)=\frac{\ln Γ(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{π^{x/2}}{Γ(1+x/2)})^{1…