A097079 Decimal expansion of the maximum value of Dedekind eta(sqrt(-1)*x), x > 0.

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

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