A388260 Decimal expansion of Integral_{x=0..1} x^2/sin(x) dx.

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

Offset

0,1

Links

Table of n, a(n) for n=0..104.

Donal F. Connon, Some exponential and trigonometric integrals involving the log gamma function, arXiv:2207.01621 [math.CA], 2022, p. 106.

Formula

Equals log(1-e^i)-log(1+e^i)+2*i*polylog(2,-e^i)-2*i*polylog(2,e^i)-2*polylog(3,-e^i)+2*polylog(3,e^i) - 7*zeta(3)/2, where i is the imaginary unit = sqrt(-1).

Example

0.54518663674217832322725204...

Mathematica

RealDigits[Re[Log[1 - E^I] - Log[1 + E^I] + 2 I PolyLog[2, -E^I] - 2 I PolyLog[2, E^I] - 2 PolyLog[3, -E^I] + 2 PolyLog[3, E^I] - (7 Zeta[3])/2], 10, 105][[1]]

Crossrefs

Sequence in context: A246729 A393373 A337029 * A293557 A123587 A018840

Adjacent sequences: A388257 A388258 A388259 * A388261 A388262 A388263

Keyword

nonn,cons

Author

Artur Jasinski, Sep 16 2025

Status

approved