A057823 Decimal expansion of q = 0.193072033..., which 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.

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

Offset

0,2

Links

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

Eric Weisstein's World of Mathematics, Dedekind Eta Function.

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: A021522 A154901 A346173 * 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