R.E. Boss wrote: > > I scanned a part of Exploratory Experimentation and Computation, > https://www.opendrive.com/files?57384074_sCfMP , where two > statements are made about a very rapidly convergent series. > > 1. The first term coincides with (pi % 8) in the first 42 digits > 2. The first 2 terms even give 500 digits > > How can these two statements be confirmed (or rejected) with J? > They can be confirmed by calculating the integrals.
Bernoulli numbers are involved among other things, and Roger's essay http://www.jsoftware.com/jwiki/Essays/Bernoulli%20Numbers gives B0=: 3 : 0 b=. ,1x for_m. }.i.x: y do. b=. b,(1+m)%~-+/b*(i.m)!1+m end. ) which can be shortened to: B0t=: [: ([ , +/@:(* i.!>:) -@% 1+])~/ }:@i.@-,1: B0 20 1 _1r2 1r6 0 _1r30 0 1r42 0 _1r30 0 5r66 0 _691r2730 0 7r6 0 _3617r510 0 43867r798 0 B0t 20x 1 _1r2 1r6 0 _1r30 0 1r42 0 _1r30 0 5r66 0 _691r2730 0 7r6 0 _3617r510 0 43867r798 0 ts 'y0=.B0 200' 1.85257 362496 ts 'y0t=.B0t 200x' 1.8853 293888 y0-:y0t 1 > > (No deadlines apply.) > > > R.E. Boss > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > > -- View this message in context: http://old.nabble.com/Challenge-12%28-%29-tp33844136s24193p33849223.html Sent from the J Programming mailing list archive at Nabble.com. ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
