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A073002 Decimal expansion of -zeta'(2) (the first derivative of the zeta function at 2). 6
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

C. F. Gauss, Disquisitiones Arithmeticae, Yale, 1965; see p. 359.

D. Huylebrouck, Generalizing Wallis' formula, American Mathematical Monthly, to appear, 2015; https://lirias.kuleuven.be/bitstream/123456789/439440/1/GeneralisingWallis.pdf

LINKS

Table of n, a(n) for n=0..104.

Simon Plouffe, Zeta(1,2) the derivative of Zeta function at 2

J. Sondow and E. W. Weisstein, MathWorld: Riemann Zeta Function

Eric Weisstein's World of Mathematics, Glaisher-Kinkelin Constant

FORMULA

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

EXAMPLE

Zeta'(2) = -0.93754825431584375370257409456786497789786028861482...

MAPLE

Zeta(1, 2); evalf(%); # R. J. Mathar, Oct 10 2011

MATHEMATICA

(* 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-Fran├žois Alcover, Apr 11 2013 *)

PROG

(PARI) -zeta'(2) \\ Charles R Greathouse IV, Mar 28, 2012

CROSSREFS

Sequence in context: A011229 A068353 A136251 * A197836 A011282 A196823

Adjacent sequences:  A072999 A073000 A073001 * A073003 A073004 A073005

KEYWORD

cons,nonn

AUTHOR

Robert G. Wilson v, Aug 03 2002

EXTENSIONS

Definition corrected by N. J. A. Sloane, Feb 19 2011

STATUS

approved

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Last modified April 18 14:05 EDT 2014. Contains 240720 sequences.