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A225125
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Decimal expansion of Integral_{x=0..Pi/2} x^3*cosec(x) dx.
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3
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1, 6, 9, 2, 9, 9, 2, 4, 6, 8, 4, 1, 3, 6, 0, 1, 2, 4, 4, 6, 7, 8, 0, 1, 3, 8, 3, 4, 8, 9, 8, 1, 0, 8, 7, 0, 8, 0, 7, 8, 6, 9, 8, 6, 7, 1, 5, 6, 8, 0, 7, 2, 3, 4, 9, 5, 6, 8, 8, 0, 1, 5, 7, 7, 8, 9, 4, 7, 6, 4, 3, 7, 2, 1, 3, 1, 9, 8, 7, 9, 8, 7, 2, 7, 9, 1, 8, 7, 3, 6, 3, 9, 6, 3, 5, 4, 4, 9, 4, 2
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OFFSET
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1,2
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COMMENTS
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The simpler Integral_{x=0..Pi/2} x*cosec(x) dx evaluates as 2*Catalan.
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LINKS
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FORMULA
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Equals 3*Catalan*Pi^2/2-1/128*(polygamma(3, 1/4)-polygamma(3, 3/4)).
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EXAMPLE
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1.6929924684136012446780138348981087080786986715680723495688...
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MATHEMATICA
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3*Catalan*Pi^2/2-1/128*(PolyGamma[3, 1/4]-PolyGamma[3, 3/4]); (* or *)
3*Catalan*Pi^2/2-3/64*(Zeta[4, 1/4]-Zeta[4, 3/4]) // RealDigits[#, 10, 100] & // First
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PROG
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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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