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A196522
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Decimal expansion of Pi*(1+sqrt(2))/8.
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1
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9, 4, 8, 0, 5, 9, 4, 4, 8, 9, 6, 8, 5, 1, 9, 9, 3, 5, 6, 8, 4, 8, 1, 5, 5, 4, 6, 6, 6, 7, 5, 2, 4, 5, 7, 2, 8, 5, 1, 4, 7, 3, 8, 8, 6, 0, 9, 3, 8, 4, 9, 5, 0, 5, 5, 0, 7, 5, 4, 2, 5, 2, 4, 9, 0, 8, 0, 3, 1, 3, 9, 9, 9, 2, 3, 2, 1, 0, 3, 6, 3, 6, 5, 0, 4, 2, 0, 2, 2, 0, 0, 1, 3, 3, 6, 0, 2, 8
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OFFSET
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0,1
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COMMENTS
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This is the mean of two Dirichlet L=functions modulo m=8 at s=1, one with character (1,0,-1,0,1,0,-1,0) as in A101455, the other with character (1,0,1,0,-1,0,-1,0).
The area of a circle circumscribed in a unit-area regular octagon. - Amiram Eldar, Nov 05 2020
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REFERENCES
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L. B. W. Jolley, Summation of series, Dover (1961), eq. 78 page 16 and eq. 264 page 48.
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LINKS
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FORMULA
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Equals (1 - 1/7) + (1/9 - 1/15) + ... + (1/(1+8*k) - 1/(7+8*k)) + ... = (A093954 + A003881)/2.
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EXAMPLE
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0.948059448968519935684815...
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MATHEMATICA
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RealDigits[Pi*(1+Sqrt[2])/8, 10, 120][[1]] (* Harvey P. Dale, May 31 2013 *)
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PROG
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(PARI) default(realprecision, 100); Pi*(1+sqrt(2))/8 \\ G. C. Greubel, Oct 05 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Pi(R)*(1+Sqrt(2))/8; // G. C. Greubel, Oct 05 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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