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 A097079 Decimal expansion of the maximum value of Dedekind eta(sqrt(-1)*x), x > 0. 3
 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, 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, 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 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS (A097078, A097079) are the coordinates of the maximum on the first graph on the linked World of Mathematics page. LINKS Stanislav Sykora, Table of n, a(n) for n = 0..2000 S. Sykora, PARI/GP scripts for optimization tasks Eric Weisstein's World of Mathematics, Dedekind Eta Function Wikipedia, Dedekind eta function FORMULA eta(A097078*i). EXAMPLE 0.83820603199292055969141859734909695266696717102845568380... MATHEMATICA FindMinimum[ 1 / DedekindEta[x*I], {x, .5235}, AccuracyGoal -> 100, MaxIterations -> 1000, WorkingPrecision -> 100] (* Ed Pegg Jr, Jul 29 2004 *) FindMaximum[q^(1/12)*QPochhammer[q^2], {q, 1/5}, WorkingPrecision -> 100][[1]] // RealDigits // First (* Jean-François Alcover, Mar 14 2016 *) PROG (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 */ (PARI) See the link. - Stanislav Sykora, Oct 25 2014 CROSSREFS Cf. A097078. Sequence in context: A217732 A089260 A109866 * A021548 A199598 A011106 Adjacent sequences:  A097076 A097077 A097078 * A097080 A097081 A097082 KEYWORD cons,nonn AUTHOR Rick L. Shepherd, Jul 24 2004 EXTENSIONS Edited by Robert G. Wilson v, Jul 29 2004 STATUS approved

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Last modified August 21 00:45 EDT 2017. Contains 290855 sequences.