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A258414 Decimal expansion of Integral_{x=0..1} Product_{k>=1} (1-x^(24*k)) dx. 3
9, 4, 9, 7, 0, 3, 1, 2, 6, 2, 9, 4, 0, 0, 9, 3, 9, 5, 2, 6, 3, 4, 9, 8, 4, 9, 1, 7, 4, 5, 7, 4, 1, 5, 1, 5, 8, 7, 3, 6, 5, 1, 9, 5, 0, 9, 0, 9, 6, 9, 2, 9, 4, 4, 8, 8, 0, 9, 1, 7, 6, 5, 4, 3, 6, 8, 3, 0, 5, 1, 9, 5, 5, 6, 8, 7, 9, 2, 8, 8, 1, 7, 2, 6, 0, 0, 6, 8, 0, 3, 2, 8, 4, 8, 3, 5, 3, 5, 0, 1, 6, 8, 7, 2, 9, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Integral_{x=-1..1} Product_{k>=1} (1-x^(24*k)) dx = Pi^2/(3*sqrt(3)) = 1.89940625258801878... . - Vaclav Kotesovec, Jun 02 2015

LINKS

Table of n, a(n) for n=0..105.

Vaclav Kotesovec, The integration of q-series

FORMULA

Equals Pi^2/(6*sqrt(3)).

EXAMPLE

0.9497031262940093952634984917457415158736519509096929448809176543683...

MAPLE

evalf(Pi^2/(6*sqrt(3)), 120);

MATHEMATICA

RealDigits[Pi^2/(6*Sqrt[3]), 10, 120][[1]]

N[Sum[(-1)^n/(12*n*(3n-1)+1), {n, -Infinity, Infinity}], 105]

CROSSREFS

Cf. A258232, A258406, A258408.

Sequence in context: A154977 A309643 A203082 * A237185 A154201 A253203

Adjacent sequences:  A258411 A258412 A258413 * A258415 A258416 A258417

KEYWORD

nonn,cons,easy

AUTHOR

Vaclav Kotesovec, May 29 2015

STATUS

approved

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Last modified August 19 08:17 EDT 2019. Contains 326115 sequences. (Running on oeis4.)