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A225119
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Decimal expansion of Integral_{x=0..Pi/2} sin(x)^(3/2) dx.
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5
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8, 7, 4, 0, 1, 9, 1, 8, 4, 7, 6, 4, 0, 3, 9, 9, 3, 6, 8, 2, 1, 6, 1, 3, 1, 9, 6, 6, 3, 0, 3, 7, 3, 1, 3, 7, 8, 9, 4, 2, 5, 1, 6, 5, 0, 4, 7, 7, 2, 0, 7, 7, 2, 0, 9, 3, 8, 9, 4, 0, 5, 6, 7, 9, 3, 3, 5, 9, 6, 8, 6, 2, 3, 5, 6, 8, 0, 4, 7, 5, 0, 0, 7, 6, 7, 6, 5, 1, 7, 7, 6, 5, 3, 8, 0, 9, 6, 9, 7, 8
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OFFSET
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0,1
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REFERENCES
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George Boros and Victor H. Moll, Irresistible integrals, Cambridge University Press (2006), p. 195.
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.3 Landau-Ramanujan constant, p. 102.
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LINKS
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FORMULA
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Equals 1/3 * sqrt(2) * ellipticK(1/2), (defined as in Mathematica).
Equals sqrt(2)/6 * Pi * hypergeom([1/2,1/2],[1],1/2).
Equals gamma(1/4)^2/(6*sqrt(2*Pi)).
Equals sqrt(Pi)*gamma(1/4)/(6*gamma(3/4)).
Equals Integral_{0..1} (1-x^2)^(1/4) dx.
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EXAMPLE
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0.87401918476403993682161319663037313789425165047720772093894...
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MAPLE
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MATHEMATICA
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RealDigits[1/3*Sqrt[2]*EllipticK[1/2], 10, 100][[1]]
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PROG
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(PARI) sqrt(Pi)*gamma(1/4)/(6*gamma(3/4)) \\ G. C. Greubel, Apr 01 2017
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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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