,catalan's ,constant ,ramanujan's       
,formula     ,catalan constant to       
#cjjjjj digits computed on ,september   
#bi1 #aiif by using a ,sun ,ultra-,sparc
 in #a day #h hour #ae min #ae sec #ee  
hsec4 ,the algorithm used is the        
standard series for ,catalan1           
accelerated by an ,euler transform4 ,the
 algorithm was implemented using the    
,li,d,i,a library for computational     
number theory and it is part of the     
multiprecision floating-point arithmetic
 of the package4  ,li,d,i,a is available
 from                                   
ftp3_/_/crypt#a4;cs4uni-sb4de_/pub_/syst
ems_/,li,d,i,a_/,li,d,i,a-#a4b4a4tgz    
http3_/_/www-jb4cs4uni-sb4de_/,li,d,i,a_
/linkhtml_/lidia_/lidia4html  ,the      
implementation of the algorithm is3     
inline void   constcatalan 7bigfloat  y7
        bigfloat p2     bigfloat t2     
int i  #a1 j  #c2 _/_/ j  #b99;i#a      
_/_/ y  t  p  #a_/b     divide 7y1 #a1  
#b72     t4assign 7y72     p4assign 7y72
      _/_/ while t is greater than the  

desired accuracy     while              
76t4isapproxzero 777                _/_/
 do         _/_/     p  p 99 7i_/j72    
_/_/     t  7t 99 i  p7 _/ j2           
_/_/     y  y  t2         _/_/     i2   
j#b2         multiply 7p1 p1 i72        
divide 7p1 p1 j72         multiply 7t1  
t1 i72         add 7t1 t1 p72           
divide 7t1 t1 j72         add 7y1 y1 t72
         i2         j  #b2              
,here is the output of the program3     
,calculating ,catalan's constant to     
#cjjjjj decimals  ,time required3 #a day
 #h hour #ae min #ae sec #ee hsec       
----------------------------------------
----------------------------------      
,additional ,,references3  ,catalan     
constant is3                            
sum77-#a799997n#a7_/7b99n-#a79999b1n#a44
;infinity7 also known under the name    
beta7#b71 see 8catalan in ,maple for    
more details4  ,the previous record was 
#bjjjjj digits1 also from ,thomas       
,papanikolaou and before that3 #ajjjjj  
digits was due to ,greg ,fee and ,simon 

,plouffe on ,august #ad1 #aiif1 by using
 a ,,sgi r#ajjjj ,power ,challenge with 
#aid ,mhz in #e4fc hours and the        
standard implementation of ,catalan on  
,maple,v1 ,release #d4 7which uses      
,greg's idea74  ,euler ,tranform3       
,references1 ,abramowitz and ,stegun1   
formula #c4f4bg page #af in ,handbook of
 ,mathematical ,functions and ,tables1  
,dover #aifd4  ,ramanujan ,notebooks1   
part ,i formula #cd4a of page #bic4     
,the series used is by putting x--      
-#a_/b 4  ,in other words the formula   
used is3 the ordinary formula for       
,catalan                                
sum77-#a799997n#a7_/7b99n#a79999b1n#j44;
infinity7  and then you apply the ,euler
 ,transform to it4  ,computation of     
,catalan's constant using ,ramanujan's  
,formula1 by ,greg ,fee1 ,,acm #aiij1   
,proceedings of the ,,isaac conference1 
#aiij1 p4 #aeg4    ,catalan constant to 
#cjjjjj digits                          
----------------------------------------
--------------------------------        

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