Catalan's Constant [Ramanujan's Formula]

by Greg Fee

Calculating Catalan's constant to 300000 decimals

Time required: 1 day 8 hour 15 min 15 sec 55 hsec

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Additional REFERENCES:

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.

Ramanujan Notebooks, part I formula 34.1 of page 293.

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)