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A258761
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Decimal expansion of Ls_5(Pi/3), the value of the 5th basic generalized log-sine integral at Pi/3 (negated).
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4
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2, 4, 0, 1, 2, 5, 3, 3, 1, 2, 5, 5, 1, 6, 9, 1, 4, 6, 1, 5, 0, 1, 5, 7, 1, 3, 9, 6, 3, 6, 3, 1, 6, 2, 6, 7, 9, 5, 0, 2, 8, 8, 4, 8, 4, 1, 0, 6, 4, 6, 3, 1, 5, 0, 2, 1, 9, 0, 1, 6, 2, 0, 7, 8, 2, 3, 3, 9, 2, 9, 9, 8, 2, 1, 7, 6, 3, 6, 8, 1, 4, 4, 4, 7, 2, 8, 9, 5, 8, 5, 8, 6, 4, 9, 1, 9, 0, 0, 1, 6, 3, 5, 2
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OFFSET
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2,1
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LINKS
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FORMULA
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-Integral_{0..Pi/3} log(2*sin(x/2))^4 dx = -1543*Pi^5/19440 + 6*Gl_{4, 1}(Pi/3), where Gl is the multiple Glaisher function.
Also equals -24 * 6F5(1/2,1/2,1/2,1/2,1/2,1/2; 3/2,3/2,3/2,3/2,3/2; 1/4) (with 6F5 the hypergeometric function).
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EXAMPLE
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-24.01253312551691461501571396363162679502884841064631502190162...
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MATHEMATICA
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RealDigits[-24*HypergeometricPFQ[Table[1/2, {6}], Table[3/2, {5}], 1/4], 10, 103] // First
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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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