  Euler's Gamma function $\Gamma$ either increases or decreases on intervals
between two consequtive critical points. The inverse of $\Gamma$ on intervals
of increase is shown to have an extension to a Pick-function and similar
results are given on the intervals of decrease, thereby answering a question by
Uchiyama. The corresponding integral representations are described. Similar
results are obtained for a class of entire functions of genus 2, and in
particular integral representations for the double gamma function and the
$G$-function of Barnes are found.
