----------------

The Catalan Constant.

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.

To do the same on your machine just type this.

> catalan := evalf(Catalan,50100):

bytes used=37569782748, alloc=5372968, time=38078.95

here are the 50000 digits (1000 lines of 50 digits each).

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 , 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 := 0.
91596559417721901505460351493238411077414937428167
21342664981196217630197762547694793565129261151062
48574422619196199579035898803325859059431594737481
15840699533202877331946051903872747816408786590902
47064841521630002287276409423882599577415088163974
70252482011560707644883807873370489900864775113225
99713434074854075532307685653357680958352602193823
23950800720680355761048235733942319149829836189977
06903640418086217941101917532743149978233976105512
24779530324875371878665828082360570225594194818097
53509711315712615804242723636439850017382875977976
53068370092980873887495610893659771940968726844441
66804621624339864838916280448281506273022742073884
31172218272190472255870531908685735423498539498309
91911596738846450861515249962423704374517773723517
75440708538464401321748392999947572446199754961975
87064007474870701490937678873045869979860644874974
64387206238513712392736304998503539223928787979063
36440323547845358519277777872709060830319943013323
16712476158709792455479119092126201854803963934243
49565375967394943547300143851807050512507488613285
64129344959502298722983162894816461622573989476231
81954200660718814275949755995898363730376753385338
13545031276817240118140721534688316835681686393272
93677586673925839540618033387830687064901433486017
29810699217995653095818715791155395603668903699049
39667538437758104931899553855162621962533168040162
73752130120940604538795076