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A196877
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Decimal expansion of Pi/2*(Pi^2/12 + (log(2))^2).
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2
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2, 0, 4, 6, 6, 2, 2, 0, 2, 4, 4, 7, 2, 7, 4, 0, 6, 4, 6, 1, 6, 9, 6, 4, 1, 0, 0, 8, 1, 7, 6, 9, 7, 3, 4, 7, 6, 6, 3, 7, 4, 4, 1, 9, 5, 3, 4, 9, 4, 6, 5, 6, 2, 6, 0, 6, 1, 0, 2, 6, 8, 5, 5, 2, 7, 2, 5, 9, 0, 6, 6, 8, 7, 9, 5, 1, 2, 1, 7, 3, 3, 6, 5, 8, 4, 6, 8, 8, 4, 6, 7, 6, 3, 2, 9, 1, 2, 5, 2, 5, 3, 4, 3, 4, 7
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OFFSET
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1,1
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COMMENTS
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The value of the integral_{x=0..Pi/2} log(sin(x))^2 dx. The value of sqrt(Pi)/2*(d^2/da^2(gamma((a+1)/2)/gamma(a/2+1))) at a=0. - Seiichi Kirikami and Peter J. C. Moses, Oct 07 2011
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REFERENCES
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I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 4th edition, 3.621.1
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LINKS
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FORMULA
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Equals Integral_{x=0..1} log(x)^2/sqrt(1-x^2) dx. - Amiram Eldar, May 27 2023
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EXAMPLE
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2.04662202447274064616964100817...
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MATHEMATICA
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RealDigits[N[Pi/2 (Pi^2/12 + Log[2]^2), 150] [[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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