Abstract
Euler’s Gamma function \(\Gamma \) either increases or decreases on intervals between two consecutive 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.
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