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%I #17 Mar 06 2013 12:11:28
%S 1,3,8,3,2,8,5,3,0,4,2,2,7,2,2,5,1,8,8,5,6,6,8,3,0,2,5,4,8,2,9,4,6,9,
%T 8,3,9,3,2,7,0,0,6,8,2,8,4,8,5,1,9,9,2,2,3,9,9,8,0,4,9,3,3,3,6,7,4,4,
%U 5,0,3,0,3,9,8,6,4,2,0,0,6,0,3,1,4,8,9,5,6,0,2,6,2,5,9,0,5,7,4,6
%N Decimal expansion of area under the curve Zeta(1/2 + t*I) from zero to its first nontrivial zero (A058303).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RiemannZetaFunctionZeros.html">Riemann Zeta Function Zeros</a>
%H <a href="/index/Z#zeta_function">Index entries for zeta function</a>.
%e 13.832853042...
%t digits = 100; NIntegrate[ Zeta[1/2 + t*I] // Abs, {t, 0, ZetaZero[1] // Im}, WorkingPrecision -> digits+5] // RealDigits[#, 10, digits]& // First (* _Jean-François Alcover_, Mar 05 2013 *)
%o (PARI) intnum(t=0,solve(s=14,15,imag(zeta(1/2+I*s))),abs(zeta(1/2+I*t))) /* Brad Chalfan (brad(AT)chalfan.net), Aug 31 2010 */
%Y Cf. A058303.
%K nonn,cons
%O 2,2
%A _Robert G. Wilson v_, May 11 2003
%E More terms from Brad Chalfan (brad(AT)chalfan.net), Aug 31 2010
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