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A102753
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Decimal expansion of (Pi^2)/2.
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9
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4, 9, 3, 4, 8, 0, 2, 2, 0, 0, 5, 4, 4, 6, 7, 9, 3, 0, 9, 4, 1, 7, 2, 4, 5, 4, 9, 9, 9, 3, 8, 0, 7, 5, 5, 6, 7, 6, 5, 6, 8, 4, 9, 7, 0, 3, 6, 2, 0, 3, 9, 5, 3, 1, 3, 2, 0, 6, 6, 7, 4, 6, 8, 8, 1, 1, 0, 0, 2, 2, 4, 1, 1, 2, 0, 9, 6, 0, 2, 6, 2, 1, 5, 0, 0, 8, 8, 6, 7, 0, 1, 8, 5, 9, 2, 7, 6, 1, 1, 5, 9, 1, 2, 0, 1
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Equals psi_1(1/2), where psi_1(x) is the second logarithmic derivative of GAMMA(x).
Also equals the volume of revolution of the sine or cosine curve for one half period, Integral_{0,Pi} Sin(x)^2 dx. - Robert G. Wilson v Dec 15 2005.
Equals sum_{k=1..infinity} 2^(2k)/k^2/binomial(2k,k) [Amdeberhan]. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 28 2007
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LINKS
| Eric Weisstein's World of Mathematics, Link to a section of Mathworld.
T. Amdeberhan, L. Medina, V. H. Moll, The integrals in Gradshteyn and Ryzhik. Part 5: Some trigonometric integrals, arXiv:0705.2379, equation 2.39.
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EXAMPLE
| 4.9348022005446793094172454999380755676568497036203953132066746881100\
224112096026215008867018592761159120129568870115720388....
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MATHEMATICA
| RealDigits[Pi^2/2, 10, 111][[1]] (from Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 15 2005)
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CROSSREFS
| Cf. A002388.
Sequence in context: A096301 A196819 A159628 * A200416 A199178 A198828
Adjacent sequences: A102750 A102751 A102752 * A102754 A102755 A102756
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KEYWORD
| cons,nonn
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AUTHOR
| Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Feb 10 2005
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