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A261069
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Decimal expansion of J_5 = Integral_{0..Pi/2} x^5/sin(x) dx.
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2
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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
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OFFSET
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1,1
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LINKS
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FORMULA
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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.
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EXAMPLE
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2.634318290518755162210315961284055055940934358931555842123212369587...
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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