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A074758
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Decimal expansion of zeta'(1/2)/zeta(1/2).
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0
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2, 6, 8, 6, 0, 9, 1, 7, 0, 9, 6, 1, 2, 8, 3, 2, 7, 9, 1, 1, 1, 6, 4, 7, 8, 7, 4, 8, 7, 2, 4, 8, 7, 1, 1, 4, 4, 5, 0, 7, 2, 6, 9, 6, 2, 5, 8, 1, 1, 7, 7, 6, 9, 2, 1, 5, 8, 4, 4, 5, 1, 3, 1, 5, 4, 9, 5, 5, 4, 7, 2, 8, 2, 8, 5, 7, 3, 3, 9, 6, 9, 8, 4, 2, 6, 0, 8, 8, 8, 6, 3, 6, 1, 3, 7, 7, 5, 5, 2, 6, 9, 1, 6, 8, 5
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OFFSET
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1,1
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REFERENCES
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S. J. Patterson, "An introduction to the theory of the Riemann Zeta-function", Cambridge studies in advanced mathematics 14, p. 29.
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LINKS
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FORMULA
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Equals log(8*Pi)/2 + EulerGamma/2 + Pi/4 = 2.6860917...
Equals (1/2) * (log(Pi) - Gamma'(1/4) / Gamma(1/4)). - Mats Granvik, Jul 30 2017
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EXAMPLE
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2.686091709612832791116478748724871144507269625811776921584451315495547282857339...
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MATHEMATICA
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RealDigits[Zeta'[1/2]/Zeta[1/2], 10, 120][[1]] (* Vaclav Kotesovec, Feb 18 2021 *)
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PROG
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(PARI) log(8*Pi)/2 + Euler/2 + Pi/4 \\ Michel Marcus, Jul 30 2017
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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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