Expressions for values of the gamma function

Details Expressions for values of the gamma function Expressions for values of the gamma function

2004-03-30

arxiv.org/abs/math/0403510v1

Kyushu J. of Math., 59(2005), pg. 267-283

Mathematics

Classical Analysis and ODEs

14 pages

Scientific paper

This paper presents expressions for gamma values at rational points with the denominator dividing 24 or 60. These gamma values are expressed in terms of 10 distinct gamma values and rational powers of $\pi$ and a few real algebraic numbers. Our elementary list of formulas can be conveniently used to evaluate, for example, algebraic Gauss hypergeometric functions by the Gauss identity. Also, algebraic independence of gamma values and their relation to the elliptic K-function are briefly discussed.

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