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Mathematics of Computation

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High-precision values of the gamma function and of some related coefficients

Authors: Arne Fransén and Staffan Wrigge
Journal: Math. Comp. 34 (1980), 553-566
MSC: Primary 65A05; Secondary 65D20
Corrigendum: Math. Comp. 37 (1981), 233-235.
MathSciNet review: 559204
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Abstract: In this paper we determine numerical values to 80D of the coefficients in the Taylor series expansion ${\Gamma ^m}(s + x) = \Sigma _0^\infty {g_k}(m,s){x^k}$ 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 $\smallint _0^\infty {(\Gamma (x))^{ - 1}}\;dx$.

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Keywords: Special functions, Gamma function, Riemann Zeta function
Article copyright: © Copyright 1980 American Mathematical Society