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A275322
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Decimal expansion of AGM(1, sqrt(2))^2/Pi.
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1
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4, 5, 6, 9, 4, 6, 5, 8, 1, 0, 4, 4, 4, 6, 3, 6, 2, 5, 3, 7, 4, 9, 6, 6, 6, 2, 2, 5, 4, 7, 6, 8, 3, 3, 3, 6, 6, 1, 1, 7, 6, 7, 7, 3, 0, 0, 1, 4, 8, 3, 1, 5, 0, 8, 3, 9, 4, 3, 6, 2, 2, 4, 7, 2, 6, 7, 4, 8, 4, 3, 5, 8, 0, 7, 0, 8, 0, 5, 3, 8, 5, 5
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OFFSET
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0,1
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COMMENTS
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Conjecture: Equals Product_{n odd} (n/(n+2) if n == 1 (mod 4), (n+2)/n otherwise) = (1/3) * (5/3) * (5/7) * (9/7) * (9/11) * (13/11) * (13/15) * (17/15) * (17/19) * (21/19) * (21/23) * (25/23) * (25/27) * ...
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LINKS
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FORMULA
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Equals 8*Pi^2/Gamma(1/4)^4 = 4*Gamma(3/4)^2/Gamma(1/4)^2. - Vaclav Kotesovec, Sep 22 2016
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EXAMPLE
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0.45694658104446362537496662254768...
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MAPLE
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MATHEMATICA
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First@ RealDigits@ N[ArithmeticGeometricMean[1, Sqrt[2]]^2/Pi, 120] (* Michael De Vlieger, Jul 26 2016 *)
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PROG
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(PARI) agm(1, sqrt(2)) ^ 2 / Pi
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); 8*Pi(R)^2/Gamma(1/4)^4; // G. C. Greubel, Oct 07 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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