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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
OFFSET
0,1
COMMENTS
(A097078, A097079) are the coordinates of the maximum on the first graph on the linked World of Mathematics page.
LINKS
Eric Weisstein's World of Mathematics, 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
KEYWORD
cons,nonn
AUTHOR
Rick L. Shepherd, Jul 24 2004
EXTENSIONS
Edited by Robert G. Wilson v, Jul 29 2004
STATUS
approved