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A215722
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Decimal expansion of Pi*(3 - gamma)/32, where gamma is Euler's constant A001620.
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1
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2, 3, 7, 8, 5, 6, 2, 9, 5, 8, 8, 6, 8, 0, 5, 5, 0, 6, 7, 4, 2, 9, 6, 2, 3, 6, 3, 0, 8, 0, 2, 3, 3, 3, 9, 4, 7, 9, 6, 3, 7, 0, 1, 2, 5, 5, 2, 3, 5, 2, 2, 3, 9, 5, 4, 4, 6, 5, 2, 1, 4, 2, 8, 0, 8, 5, 1, 8, 5, 6, 2, 4, 6, 6, 3, 3, 9, 3, 2, 7, 9, 9, 1, 3, 7, 1, 1, 2, 1, 7, 8, 7, 9, 8, 3, 7, 5, 2, 3, 8, 3, 7, 7, 2, 9, 5, 5, 5, 3, 4, 0, 9
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OFFSET
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0,1
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COMMENTS
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Volchkov shows that this is equal to integral(t=0..infinity, (1-12t^2)/(1+4t^2)^3) * integral(s=1/2..infinity, log |zeta(s + it)|) if and only if the Riemann hypothesis holds.
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REFERENCES
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V. V. Volchkov, On an equality equivalent to the Riemann hypothesis, Ukranian Mathematical Journal 47:3 (1995), pp. 491-493. doi:10.1007/BF01056314
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LINKS
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EXAMPLE
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0.237856295886805506742962363080233394796370125523522395446521428085...
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MATHEMATICA
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RealDigits[Pi*(3 - EulerGamma)/32, 10, 100][[1]] (* G. C. Greubel, Aug 27 2018 *)
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PROG
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(PARI) Pi*(3-Euler)/32
(Magma) R:= RealField(100); Pi(R)*(3 - EulerGamma(R))/32; // 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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