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A059750
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Decimal expansion of zeta(1/2) (negated).
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9
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1, 4, 6, 0, 3, 5, 4, 5, 0, 8, 8, 0, 9, 5, 8, 6, 8, 1, 2, 8, 8, 9, 4, 9, 9, 1, 5, 2, 5, 1, 5, 2, 9, 8, 0, 1, 2, 4, 6, 7, 2, 2, 9, 3, 3, 1, 0, 1, 2, 5, 8, 1, 4, 9, 0, 5, 4, 2, 8, 8, 6, 0, 8, 7, 8, 2, 5, 5, 3, 0, 5, 2, 9, 4, 7, 4, 5, 0, 0, 6, 2, 5, 2, 7, 6, 4, 1, 9, 3, 7, 5, 4, 6, 3, 3, 5, 6, 8, 1
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OFFSET
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1,2
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COMMENTS
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Zeta(1/2) can be calculated as a limit similar to the limit for the Euler-Mascheroni constant or Euler gamma. [Mats Granvik Nov 14 2012]
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,5000
Eric Weisstein's World of Mathematics, Riemann Zeta Function
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FORMULA
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Zeta(1/2) = Limit of Sum from n=1 to n=k of 1/n^(1/2) -2*k^(1/2), as k goes to infinity. (According to Mathematica 8). [Mats Granvik Nov 14 2012]
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EXAMPLE
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-1.4603545088095868128894991525152980124672293310125814905428860878...
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MAPLE
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Digits := 120; evalf(Zeta(1/2));
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MATHEMATICA
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RealDigits[ Zeta[1/2], 10, 111][[1]] (* Robert G. Wilson v, Oct 11 2005 *)
RealDigits[N[Limit[Sum[1/Sqrt[n], {n, 1, k}] - 2*Sqrt[k], k -> Infinity], 90]][[1]] (* Mats Granvik Nov 14 2012 *)
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PROG
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(PARI) { default(realprecision, 5080); x=-zeta(1/2); for (n=1, 5000, d=floor(x); x=(x-d)*10; write("b059750.txt", n, " ", d)); } [Harry J. Smith, Jun 29 2009]
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CROSSREFS
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Cf. A161688 (continued fraction).
Sequence in context: A204017 A021960 A096256 * A117036 A016723 A194183
Adjacent sequences: A059747 A059748 A059749 * A059751 A059752 A059753
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KEYWORD
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nonn,cons
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AUTHOR
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Peter Walker (peterw(AT)aus.ac.ae), Feb 11 2001
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EXTENSIONS
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Sign of the constant reversed by R. J. Mathar, Feb 05 2009
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STATUS
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approved
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