  For $0\neq x>-1$ let $$\Delta(x)={{\ln \Gamma(x+1)} \over x}.$$ Recently
Adell and Alzer proved the complete monotonicity of $\Delta'$ on $(-1,\infty)$
by giving an integral representation of $(-1)^n \Delta^{(n+1)}(x)$ in terms of
the Hurwitz zeta function $\zeta(s,a)$. We reprove this integral representation
in different ways, and then re-express it in terms of fractional part
integrals. Special cases then have explicit evaluations. Other relations for
$\Delta^{(n+1)}(x)$ are presented, including its leading asymptotic form as $x
\to \infty$.
