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%I #16 Mar 14 2016 07:39:32
%S 8,3,8,2,0,6,0,3,1,9,9,2,9,2,0,5,5,9,6,9,1,4,1,8,5,9,7,3,4,9,0,9,6,9,
%T 5,2,6,6,6,9,6,7,1,7,1,0,2,8,4,5,5,6,8,3,8,0,1,1,1,6,6,1,9,0,5,8,0,7,
%U 3,3,3,4,0,1,6,0,2,0,4,2,4,0,3,3,1,5,1,8,6,3,3,3,7,2,0,7,0,3,1,2
%N Decimal expansion of the maximum value of Dedekind eta(sqrt(-1)*x), x > 0.
%C (A097078, A097079) are the coordinates of the maximum on the first graph on the linked World of Mathematics page.
%H Stanislav Sykora, <a href="/A097079/b097079.txt">Table of n, a(n) for n = 0..2000</a>
%H S. Sykora, <a href="https://oeis.org/wiki/File:OptimizationFunctions.txt">PARI/GP scripts for optimization tasks</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DedekindEtaFunction.html">Dedekind Eta Function</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Dedekind_eta_function">Dedekind eta function</a>
%F eta(A097078*i).
%e 0.83820603199292055969141859734909695266696717102845568380...
%t FindMinimum[ 1 / DedekindEta[x*I], {x, .5235}, AccuracyGoal -> 100, MaxIterations -> 1000, WorkingPrecision -> 100] (* _Ed Pegg Jr_, Jul 29 2004 *)
%t FindMaximum[q^(1/12)*QPochhammer[q^2], {q, 1/5}, WorkingPrecision -> 100][[1]] // RealDigits // First (* _Jean-François Alcover_, Mar 14 2016 *)
%o (PARI) /* Click on cons keyword link of A097078 to copy x value */ x= {value copied above} eta(x*I,1) /* Note: nonzero flag (1 here) must be used */
%o (PARI) See the link. - _Stanislav Sykora_, Oct 25 2014
%Y Cf. A097078.
%K cons,nonn
%O 0,1
%A _Rick L. Shepherd_, Jul 24 2004
%E Edited by _Robert G. Wilson v_, Jul 29 2004
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