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A225119
Decimal expansion of Integral_{x=0..Pi/2} sin(x)^(3/2) dx.
5
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
OFFSET
0,1
REFERENCES
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.
FORMULA
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.
Equals Integral_{0..1} sqrt(1-x^4) dx. - Charles R Greathouse IV, Aug 21 2017
Equals (2/3)*A085565. - Peter Bala, Oct 27 2019
EXAMPLE
0.87401918476403993682161319663037313789425165047720772093894...
MAPLE
evalf((1/3)*sqrt(2)*EllipticK(1/sqrt(2)), 120); # Vaclav Kotesovec, Apr 22 2015
MATHEMATICA
RealDigits[1/3*Sqrt[2]*EllipticK[1/2], 10, 100][[1]]
PROG
(PARI) sqrt(Pi)*gamma(1/4)/(6*gamma(3/4)) \\ G. C. Greubel, Apr 01 2017
CROSSREFS
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved