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A073002
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Decimal expansion of -zeta'(2) (the first derivative of the zeta function at 2).
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6
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9, 3, 7, 5, 4, 8, 2, 5, 4, 3, 1, 5, 8, 4, 3, 7, 5, 3, 7, 0, 2, 5, 7, 4, 0, 9, 4, 5, 6, 7, 8, 6, 4, 9, 7, 7, 8, 9, 7, 8, 6, 0, 2, 8, 8, 6, 1, 4, 8, 2, 9, 9, 2, 5, 8, 8, 5, 4, 3, 3, 4, 8, 0, 3, 6, 0, 4, 4, 3, 8, 1, 1, 3, 1, 2, 7, 0, 7, 5, 2, 2, 7, 9, 3, 6, 8, 9, 4, 1, 5, 1, 4, 1, 1, 5, 1, 5, 1, 7, 4, 9, 3, 1, 1, 3
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OFFSET
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0,1
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REFERENCES
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C. F. Gauss, Disquisitiones Arithmeticae, Yale, 1965; see p. 359.
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LINKS
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Table of n, a(n) for n=0..104.
Simon Plouffe, Zeta(1,2) the derivative of Zeta function at 2
Eric Weisstein's World of Mathematics, Riemann Zeta Function
Eric Weisstein's World of Mathematics, Glaisher-Kinkelin Constant
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FORMULA
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Sum_{n >= 1} log n / n^2. - N. J. A. Sloane, Feb 19 2011
Pi^2(gamma + log(2Pi) - 12 log A)/6, where A is the Glaisher-Kinkelin constant. - Charles R Greathouse IV, May 06 2013
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EXAMPLE
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Zeta'(2) = -0.93754825431584375370257409456786497789786028861482...
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MAPLE
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Zeta(1, 2); evalf(%); # R. J. Mathar, Oct 10 2011
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MATHEMATICA
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(* first do *) Needs["NumericalMath`NLimit`"], (* then *) RealDigits[ N[ ND[ Zeta[z], z, 2, WorkingPrecision -> 200, Scale -> 10^-20, Terms -> 20], 111]][[1]] (* from Eric W. Weisstein, May 20 2004 *)
(* from version 6 on *) RealDigits[-Zeta'[2], 10, 105] // First (* or *) RealDigits[-Pi^2/6*(EulerGamma - 12*Log[Glaisher] + Log[2*Pi]), 10, 105] // First (* Jean-François Alcover, Apr 11 2013 *)
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PROG
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(PARI) -zeta'(2) \\ Charles R Greathouse IV, Mar 28, 2012
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CROSSREFS
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Sequence in context: A011229 A068353 A136251 * A197836 A011282 A196823
Adjacent sequences: A072999 A073000 A073001 * A073003 A073004 A073005
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KEYWORD
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cons,nonn,changed
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AUTHOR
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Robert G. Wilson v, Aug 03 2002
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EXTENSIONS
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Definition corrected by N. J. A. Sloane, Feb 19 2011
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STATUS
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approved
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