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High-Precision Values of the Gamma Function and of Some Related Coefficients

Arne Fransen and Staffan Wrigge
Mathematics of Computation
Vol. 34, No. 150 (Apr., 1980), pp. 553-566
DOI: 10.2307/2006104
Stable URL: http://www.jstor.org/stable/2006104
Page Count: 14
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High-Precision Values of the Gamma Function and of Some Related Coefficients
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Abstract

In this paper we determine numerical values to 80D of the coefficients in the Taylor series expansion $\Gamma^m(s + x) = \sum^\infty_0 g_k(m, s)x^k$ for certain values of $m$ and $s$ and use these values to calculate $\Gamma(p/q) (p, q = 1, 2,\ldots, 10; p < q)$ and $\min_{x>0}\Gamma(x)$ to 80D. Finally, we obtain a high-precision value of the integral $\int^\infty_0(\Gamma(x))^{-1} dx$.

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