Inverses of Gamma Functions
Copyright policy )Inverses of Gamma Functions
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 $G$-function of Barnes are found.
20 pages
- University of Copenhagen Denmark
- University of Copenhagen Denmark
Pick function, Mathematics - Complex Variables, Special classes of entire functions of one complex variable and growth estimates, 30D15, gamma function, Double gamma function, Entire function, Mathematics - Classical Analysis and ODEs, Gamma function, double gamma function, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Integral representation, Inverse, Complex Variables (math.CV), Gamma, beta and polygamma functions, Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane, entire functions
Pick function, Mathematics - Complex Variables, Special classes of entire functions of one complex variable and growth estimates, 30D15, gamma function, Double gamma function, Entire function, Mathematics - Classical Analysis and ODEs, Gamma function, double gamma function, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Integral representation, Inverse, Complex Variables (math.CV), Gamma, beta and polygamma functions, Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane, entire functions
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