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A173623
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Decimal expansion of Pi*log(2)/2.
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10
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1, 0, 8, 8, 7, 9, 3, 0, 4, 5, 1, 5, 1, 8, 0, 1, 0, 6, 5, 2, 5, 0, 3, 4, 4, 4, 4, 9, 1, 1, 8, 8, 0, 6, 9, 7, 3, 6, 6, 9, 2, 9, 1, 8, 5, 0, 1, 8, 4, 6, 4, 3, 1, 4, 7, 1, 6, 2, 8, 9, 7, 6, 2, 6, 5, 9, 7, 1, 5, 4, 2, 7, 4, 5, 8, 8, 3, 7, 0, 9, 9, 3, 2, 1, 5, 1, 6, 4, 4, 8, 0, 8, 0, 5, 3, 3, 1, 5, 1, 2, 5, 2, 8, 8, 0
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OFFSET
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1,3
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REFERENCES
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Paul J. Nahin, Inside Interesting Integrals, Springer 2015, ISBN 978-1493912766.
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LINKS
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FORMULA
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Equals abs(Integral {x=0..Pi/2} log(sin(x)) dx).
Equals Sum_{k>=0} binomial(2*k,k)/(4^k*(2*k+1)^2) = Sum_{k>=0} A000984(k)/A164583(k).
Equals Integral_{x=0..1} arcsin(x)/x dx.
Equals Integral_{x=0..Pi/2} x*cot(x) dx. (End)
Equals Integral_{x = 0..1} log(x + 1/x)/(1 + x^2) dx (Nahin, 2.4.4) = (1/2)*Integral_{x = 0..oo} log(x^2 + 4)/(x^2 + 4) dx = (1/2)*Integral_{x = 0..oo} log(x^2 + 1)/(x^2 + 1) dx = Integral_{x = 0..oo} log(x^2 + 64)/(x^2 + 64) dx. - Peter Bala, Jul 22 2022
Equals 3F2(1/2,1/2,1/2 ; 3/2,3/2 ; 1). - R. J. Mathar, Aug 19 2024
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EXAMPLE
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1.08879304515180106525034444...
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MAPLE
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Pi/2*log(2) ; evalf(%) ;
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MATHEMATICA
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RealDigits[Pi*Log[2]/2, 10, 100][[1]] (* Amiram Eldar, Jul 13 2020 *)
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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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