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Numerical algorithms for problems in analysis and algebra, scientific computation
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show that $ \frac{\Gamma(\frac{1}{24})\Gamma(\frac{11}{24})}{\Gamma(\frac{5}{24})\Gamma(\fra...
As a consequence of Euler's refection and Gauss's multiplication formulas (mentioned in the Elkies answer), all values $\Gamma(a)$ with $24a\in\mathbb{Z}$ can be expressed algebraically in terms of th …