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) and then you apply the Euler
Transform to it.

Computation of Catalan's constant using Ramanujan's Formula, by
Greg Fee, ACM 1990, Proceedings of the ISAAC conference, 1990, p. 157.



Catalan constant to 300000 digits
------------------------------------------------------------------------
.91596559417721901505460351493238411077414937428167213426649811962176301977625\
476947935651292611510624857442261919619957903589880332585905943159473748115840\
699533202877331946051903872747816408786590902470648415216300022872764094238825\
995774150881639747025248201156070764488380787337048990086477511322599713434074\
854075532307685653357680958352602193823239508007206803557610482357339423191498\
298361899770690364041808621794110191753274314997823397610551224779530324875371\
878665828082360570225594194818097535097113157126158042427236364398500173828759\
779765306837009298087388749561089365977194096872684444166804621624339864838916\
280448281506273022742073884311722182721904722558705319086857354234985394983099\
191159673884645086151524996242370437451777372351775440708538464401321748392999\
947572446199754961975870640074748707014909376788730458699798606448749746438720\
623851371239273630499850353922392878797906336440323547845358519277777872709060\
830319943013323167124761587097924554791190921262018548039639342434956537596739\