OFFSET
1,3
REFERENCES
Pablo Fernandez Refolio, Problem 12180, The American Mathematical Monthly 127, April 2020, p. 373.
FORMULA
Equals 2/Pi + sqrt(Pi/2) / Gamma(3/4)^2 - sqrt(2) * Gamma(3/4)^2 / Pi^(3/2).
Equals hypergeom([1/4, 1/4, 3/4, 3/4], [1/2, 1, 3/2], 1).
EXAMPLE
1.0898667322907479353258017958072963604855169777781363398319609472070578367683...
MAPLE
evalf(2/Pi + sqrt(Pi/2) / GAMMA(3/4)^2 - sqrt(2) * GAMMA(3/4)^2 / Pi^(3/2), 120);
MATHEMATICA
RealDigits[2/Pi + Sqrt[Pi/2]/Gamma[3/4]^2 - Sqrt[2]*Gamma[3/4]^2/Pi^(3/2), 10, 100][[1]]
N[HypergeometricPFQ[{1/4, 1/4, 3/4, 3/4}, {1/2, 1, 3/2}, 1], 120]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Vaclav Kotesovec, Nov 12 2020
STATUS
approved