OFFSET
0,1
LINKS
J. M. Borwein, R. Girgensohn, Evaluations of binomial series, Aequat. Math. 70 (2005) 25-36, Eq. (39).
EXAMPLE
0.4143220443218203918650039438312489508452...
MATHEMATICA
HypergeometricPFQ[{1, 3/2, 2}, {4/3, 5/3}, 4/27]/3 // RealDigits[#, 10, 105]& // First (* Jean-François Alcover, Feb 18 2014 *)
Chop[N[(1/3174)*(552 + 2*(-110*69^(2/3)*(2/(-4761 + 997*Sqrt[69]))^(1/3) + 2^(2/3)*(69*(-4761 + 997*Sqrt[69]))^(1/3))* Log[997 + (1/3)*(26757728271/2 - (2973080919*Sqrt[69])/2)^(1/3) + (997*((1/2)*(9 + Sqrt[69]))^(1/3))/3^(2/3)] + (110*69^(2/3)*(1 - I*Sqrt[3])*(2/(-4761 + 997*Sqrt[69]))^(1/3) - 2^(2/3)*(1 + I*Sqrt[3])* (69*(-4761 + 997*Sqrt[69]))^(1/3))* Log[997 - (1/6)*(1 + I*Sqrt[3])*(26757728271/2 - (2973080919*Sqrt[69])/2)^(1/3) - (997*(1 - I*Sqrt[3])*((1/2)*(9 + Sqrt[69]))^(1/3))/(2*3^(2/3))] + (110*69^(2/3)*(1 + I*Sqrt[3])*(2/(-4761 + 997*Sqrt[69]))^(1/3) - 2^(2/3)*(1 - I*Sqrt[3])* (69*(-4761 + 997*Sqrt[69]))^(1/3))* Log[997 - (1/6)*(1 - I*Sqrt[3])*(26757728271/2 - (2973080919*Sqrt[69])/2)^(1/3) - (997*(1 + I*Sqrt[3])*((1/2)*(9 + Sqrt[69]))^(1/3))/(2*3^(2/3))]), 120]] (* Vaclav Kotesovec, Nov 14 2020 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
R. J. Mathar, Sep 27 2013
EXTENSIONS
More terms from Jean-François Alcover, Feb 18 2014
STATUS
approved