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A365318
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Decimal expansion of negative imaginary part of Gamma(exp(i*Pi/3)).
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5
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5, 1, 7, 2, 7, 9, 0, 9, 9, 4, 7, 4, 8, 4, 0, 1, 5, 1, 5, 9, 3, 3, 2, 3, 5, 0, 1, 7, 1, 5, 4, 1, 9, 0, 7, 2, 2, 1, 8, 4, 7, 0, 9, 0, 3, 3, 1, 4, 1, 7, 5, 9, 0, 8, 7, 9, 8, 3, 2, 3, 2, 2, 6, 4, 4, 9, 9, 0, 0, 3, 6, 0, 0, 3, 2, 7, 5, 1, 7, 7, 5, 8, 6, 8, 0, 1, 6, 4, 2, 2, 6, 3, 6, 1, 1, 6, 1, 1, 1, 0, 9, 6, 6, 0, 9, 2
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OFFSET
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0,1
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LINKS
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FORMULA
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Equals sqrt(Pi*sech(Pi*sqrt(3)/2))*sin(2*theta(sqrt(3)/2)+(sqrt(3)/2)*log(2*Pi)+arctan(tanh(Pi*sqrt(3)/4)) where theta is Riemann-Siegel theta function.
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EXAMPLE
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0.51727909947484...
Gamma(cos(Pi/3) + I*sin(Pi/3)) = 0.37980489179139...-I*0.51727909947484...
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MATHEMATICA
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RealDigits[-Im[Gamma[Cos[Pi/3] + I Sin[Pi/3]]], 10, 106][[1]]
(* or *)
RealDigits[Sqrt[Pi/Cosh[Pi Sqrt[3]/2]] Sin[2 RiemannSiegelTheta[Sqrt[3]/2] + ArcTan[Tanh[Pi Sqrt[3]/4]] + Sqrt[3] Log[2 Pi]/2], 10, 106][[1]]
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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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