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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 March 24 05:55 EDT 2017. Contains 283984 sequences.