Greg Fee

“ The implementation of the algorithm is:
inline void
const_catalan (bigfloat & y)
{
bigfloat p;
bigfloat t;
int i = 1, j = 3; // j = 2*i+1
// y = t = p = 1/2 divide (y, 1, 2) ; t.assign (y) ; p.assign (y) ;
// while t is greater than the desired accuracy
while (!t.is_approx_zero () )
{
// do
// p = p * (i/j) ;
// t = (t * i + p) / j;
// y = y + t;
// i++; j+=2;
multiply (p, p, i) ;
divide (p, p, j) ;
multiply (t, t, i) ;
add (t, t, p) ;
divide (t, t, j) ;
add (y, y, t) ”

“ Catalan constant is: sum ( (-1) ** (n+1) / (2*n-1) **2,n=1..infinity) also known under the name beta (2) , see ?catalan in Maple for more details.
The previous record was 200000 digits, also from Thomas Papanikolaou and before that: 100000 digits was due to Greg Fee and Simon Plouffe on August 14, 1996, by using a SGI r10000 Power Challenge with 194 Mhz in 5.63 hours and the standard implementation of Catalan on MapleV, Release 4. (which uses Greg's idea) .
Euler Tranform: References, Abramowitz and Stegun, formula 3.6.27 page 16 in Handbook of Mathematical Functions and Tables, Dover 1964. ”