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A245273 Decimal expansion of zeta''(0)+2, the coefficient of z^2 in the Laurent expansion of zeta(z) at the origin. 1

%I #5 Jul 16 2014 06:02:36

%S 0,0,6,3,5,6,4,5,5,9,0,8,5,8,4,8,5,1,2,1,0,1,0,0,0,2,6,7,2,9,9,6,0,4,

%T 3,8,1,9,8,9,9,4,9,1,0,1,6,0,9,1,9,8,8,1,1,6,9,8,6,8,2,8,0,8,5,7,7,6,

%U 0,0,7,8,3,9,8,0,8,5,3,4,2,7,6,4,8,7,0,5,6,0,3,2,8,0,8,3,9,2,4,7,2,6,6,3,7,4,2

%N Decimal expansion of zeta''(0)+2, the coefficient of z^2 in the Laurent expansion of zeta(z) at the origin.

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.21 Stieltjes Constants, p. 168.

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/StieltjesConstants.html">Stieltjes Constants</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Stieltjes_constants">Stieltjes constants</a>

%F -Pi^2/24 - log(2*Pi)^2/2 + gamma^2/2 + gamma(1) + 2, where gamma is Euler's constant and gamma(1) is the first Stieltjes constant.

%e -0.00635645590858485121010002672996043819899491016091988116986828085776...

%t Join[{0, 0}, RealDigits[Zeta''[0]+2, 10, 105] // First]

%Y Cf. A082633(gamma(1)), A110544(coefficient of z).

%K nonn,cons,easy

%O 0,3

%A _Jean-François Alcover_, Jul 16 2014

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Last modified March 28 21:57 EDT 2024. Contains 371254 sequences. (Running on oeis4.)