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A261069
Decimal expansion of J_5 = Integral_{0..Pi/2} x^5/sin(x) dx.
2
2, 6, 3, 4, 3, 1, 8, 2, 9, 0, 5, 1, 8, 7, 5, 5, 1, 6, 2, 2, 1, 0, 3, 1, 5, 9, 6, 1, 2, 8, 4, 0, 5, 5, 0, 5, 5, 9, 4, 0, 9, 3, 4, 3, 5, 8, 9, 3, 1, 5, 5, 5, 8, 4, 2, 1, 2, 3, 2, 1, 2, 3, 6, 9, 5, 8, 7, 1, 8, 0, 4, 6, 4, 0, 9, 5, 7, 1, 9, 1, 2, 7, 0, 2, 5, 2, 4, 0, 7, 0, 9, 7, 8, 2, 6, 6, 0, 5, 6, 2, 9, 8, 6
OFFSET
1,1
LINKS
J. M. Borwein, I. J. Zucker and J. Boersma, The evaluation of character Euler double sums, The Ramanujan Journal, April 2008, Volume 15, Issue 3, pp 377-405, see p. 13.
FORMULA
J_5 = (5*Catalan*Pi^4)/8 - (29*i*Pi^6)/2016 - 30*i*Pi^2*PolyLog(4, -i) + 240*i*PolyLog(6, -i).
Also equals (40*Pi^2*(32*Catalan*Pi^2 - PolyGamma(3, 1/4) + PolyGamma(3, 3/4)) + PolyGamma(5, 1/4) - PolyGamma(5, 3/4))/2048.
EXAMPLE
2.634318290518755162210315961284055055940934358931555842123212369587...
MATHEMATICA
J5 = (5*Catalan*Pi^4)/8 - (29*I*Pi^6)/2016 - 30*I*Pi^2*PolyLog[4, -I] +
240*I*PolyLog[6, -I]; RealDigits[J5 // Re, 10, 103] // First
RealDigits[NIntegrate[x^5/Sin[x], {x, 0, Pi/2}, WorkingPrecision->120]][[1]] (* Harvey P. Dale, Aug 09 2023 *)
CROSSREFS
Cf. A006752 (J_1 / 2 = Catalan's constant), A245073 (J_2), A225125 (J_3), A261068 (J_4).
Sequence in context: A066098 A299160 A123733 * A236557 A359243 A262943
KEYWORD
nonn,cons
AUTHOR
STATUS
approved