Inverses of gamma functions
Complex Variables
2013-09-10 v1 Classical Analysis and ODEs
Abstract
Euler's Gamma function either increases or decreases on intervals between two consequtive critical points. The inverse of 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 -function of Barnes are found.
Cite
@article{arxiv.1309.2167,
title = {Inverses of gamma functions},
author = {Henrik L. Pedersen},
journal= {arXiv preprint arXiv:1309.2167},
year = {2013}
}
Comments
20 pages