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A020759
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Decimal expansion of (-1)*Gamma'(1/2)/Gamma(1/2) where Gamma(x) denotes the Gamma function.
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17
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1, 9, 6, 3, 5, 1, 0, 0, 2, 6, 0, 2, 1, 4, 2, 3, 4, 7, 9, 4, 4, 0, 9, 7, 6, 3, 3, 2, 9, 9, 8, 7, 5, 5, 5, 6, 7, 1, 9, 3, 1, 5, 9, 6, 0, 4, 6, 6, 0, 4, 3, 4, 1, 0, 7, 0, 4, 7, 1, 2, 7, 2, 5, 3, 8, 7, 1, 6, 5, 4, 9, 7, 0, 7, 1, 7, 0, 5, 4, 1, 0, 2, 1, 4, 8, 6, 7, 3, 7, 1, 7, 2, 8, 4, 5, 8, 4, 1, 2, 4, 5, 9, 8, 6, 3
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OFFSET
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1,2
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COMMENTS
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), 6.3.3, p. 258. - Robert G. Wilson v, Jun 20 2011
S. J. Patterson, An introduction to the theory of the Riemann zeta function, Cambridge studies in advanced mathematics no. 14, p. 135.
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LINKS
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FORMULA
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Gamma'(1/2)/Gamma(1/2) = -EulerGamma - 2*log(2) = -1.9635100260214234794... where EulerGamma is the Euler-Mascheroni constant (A001620).
Equals lim_{n->oo} (Sum_{k=0..n} 1/(k+1/2) - log(n)). - Amiram Eldar, Mar 04 2023
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EXAMPLE
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1.96351002602142347944097633299875556719315960466...
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MAPLE
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MATHEMATICA
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PROG
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(PARI) Euler+2*log(2)
(Magma) R:=RealField(100); EulerGamma(R) + 2*Log(2); // G. C. Greubel, Aug 27 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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