

A217708


Decimal expansion of integral_{0, Pi/4} log(sin(x))^3 dx.


0



6, 0, 3, 7, 5, 8, 1, 1, 0, 6, 3, 0, 9, 5, 9, 8, 1, 7, 0, 2, 6, 7, 4, 3, 6, 8, 9, 2, 6, 5, 0, 2, 6, 7, 4, 6, 7, 5, 5, 0, 3, 9, 8, 2, 8, 5, 8, 8, 8, 6, 8, 6, 2, 7, 1, 7, 5, 1, 8, 0, 4, 9, 0, 1, 3, 5, 5, 8, 7, 4, 2, 2, 1, 2, 7, 0, 1, 6, 0, 6, 7, 4, 0, 9, 7, 6, 9, 3, 5, 9, 7, 6, 6, 7, 5, 9, 9, 6, 8, 2
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OFFSET

1,1


COMMENTS

Curiously, this integral from 0 to Pi/4 is far more difficult to evaluate by hand than the same integral from 0 to Pi/2.


LINKS



EXAMPLE

6.037581106...


MATHEMATICA

(1/8)*((Log[2]^2)*(Pi*Log[2] + 3*Catalan)  4*Sqrt[2]*(6*HypergeometricPFQ[{1/2, 1/2, 1/2, 1/2, 1/2}, {3/2, 3/2, 3/2, 3/2}, 1/2] + HypergeometricPFQ[{1/2, 1/2, 1/2, 1/2}, {3/2, 3/2, 3/2}, 1/2]*Log[8])) // RealDigits[#, 10, 100] & // First
RealDigits[Integrate[Log[Sin[x]]^3, {x, 0, Pi/4}], 10, 120][[1]] (* Harvey P. Dale, Jun 08 2021 *)


CROSSREFS

Cf. A196878 (the same integral from 0 to Pi/2)


KEYWORD



AUTHOR



STATUS

approved



