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A057823 The number q = 0.193072033... is the value of q which gives the maximum of the Dedekind eta function eta(q) := q^(1/12) * product_{n>=1} (1-q^(2n)) for q between 0 and 1. 2
1, 9, 3, 0, 7, 2, 0, 3, 3, 9, 5, 7, 4, 1, 0, 9, 7, 8, 9, 2, 2, 9, 4, 1, 6, 8, 5, 4, 2, 1, 2, 6, 2, 2, 5, 4, 5, 7, 0, 5, 0, 7, 7, 6, 0, 9, 7, 8, 7, 0, 4, 7, 2, 1, 6, 0, 9, 8, 0, 8, 9, 8, 9, 0, 7, 7, 7, 4, 6, 8, 4, 0, 5, 6, 7, 8, 7, 4, 9, 2, 5, 7, 0, 2, 8, 9, 6, 3, 9, 2, 7, 9, 3, 3, 6, 0, 8, 8, 0, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..99.

E. Weisstein, Dedekind Eta Function, MathWorld.

FORMULA

Equals sqrt(A211342). - Vaclav Kotesovec, Jul 02 2017

EXAMPLE

0.19307203395741097892294168542126225457050776097870...

MATHEMATICA

RealDigits[FindRoot[D[q^(1/12)*Product[(1-q^(2 n)), {n, 100}], q] == 0, {q, 0.2}, WorkingPrecision -> 200][[1, 2]]][[1]]

q /. Last @ FindMaximum[ DedekindEta[ -I*Log[q]/Pi], {q, 1/5}, WorkingPrecision -> 200] // RealDigits[#][[1]][[1 ;; 100]]&  (* Jean-François Alcover, Feb 05 2013 *)

q0 = q /. FindMaximum[q^(1/12)*QPochhammer[q^2], {q, 1/5}, WorkingPrecision -> 200][[2]]; RealDigits[q0, 10, 100][[1]] (* Jean-François Alcover, Nov 25 2015 *)

CROSSREFS

Cf. A211342.

Sequence in context: A199605 A021522 A154901 * A011461 A302716 A198546

Adjacent sequences:  A057820 A057821 A057822 * A057824 A057825 A057826

KEYWORD

cons,nonn,easy,nice

AUTHOR

Peter L. Walker (peterw(AT)aus.ac.ae), Nov 24 2000

EXTENSIONS

More terms from Vladeta Jovovic, Jun 19 2004

STATUS

approved

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Last modified July 23 22:38 EDT 2019. Contains 325278 sequences. (Running on oeis4.)