“ It comes from formula 34.1 of page 293 of Ramanujan Notebooks, part I, the series used is by putting x—> -1/2 . In other words the formula used is: the ordinary formula for Catalan sum ( (-1) ** (n+1) / (2*n+1) **2,n=0..infinity) and then you apply the Euler Transform to it: ref: Abramowitz & Stegun page 16. The article of Greg Fee that took those formulas appear in Computation of Catalan's constant using Ramanujan's Formula, by Greg Fee, ACM 1990, Proceedings of the ISAAC conference, 1990 (MAYBE 1989) , held in Tokyo. ”

“ Catalan evaluation
170000 digits of gamma or Euler constant
The Artin's Constant
The Backhouse Constant
Zeta (3) or Apery Constant
Zeta (1,2) or the derivative of Zeta function at 2
Feigenbaum reduction parameter
Feigenbaum bifurcation velocity constant
Franson-Robinson constant
The Gauss-Kusmin-Wirsing constant
Khinchin constant
Landau-Ramanujan constant
The twin primes constant
The Lengyel constant
The Levy constant
The golden ratio: (1+sqrt (5) ) /2 to 20000 places. ”

“ As calculated by Greg Fee using Maple Release 3 standard Catalan evaluation. This implementation uses 1 bit/term series of Ramanujan. Calculated on April 25 1996 in approx. 10 hours of CPU on a SGI R4000 machine. ”