As Murray points out, there are indeed faster means of computing Riemann's zeta function.
Carl Siegel found the formula now known as the Riemann-Siegel formula when working through some of Riemann's hard to decipher handwritten notes. That formula is (I believe) the basis of modern numerical computations of the zeta function. http://en.wikipedia.org/wiki/Riemann–Siegel_formula There's a wonderful book by H.M. Edwards with (almost) everything you wanted to ask about the zeta function. -Dan On 9 Mar 2014, at 12:25, Dan Abell wrote: > so > > zeta =: [:+/(%@^~>:@i.) > > then > > 2 zeta 2e5 > 1.64493 > 3 zeta 1e5 > 1.20206 > > this also works for non-integer arguments: > > 3.5 zeta 1e5 > 1.12673 > 3.5j0.5 zeta 1e5 > 1.11256j_0.053509 > > Cheers, > -Dan > > On 9 Mar 2014, at 11:54, Aai wrote: > >> in fact something like: >> >> 2 +/@:(%@^~) 1+i.100000 >> 1.64492 >> >> -- >> Met vriendelijke groet, >> @@i = Arie Groeneveld >> >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm -- Dan T. Abell :: dabell at txcorp dot com :: 303.444.2452 Tech-X Corp., 5621 Arapahoe Ave, Ste A, Boulder CO 80303 http://www.txcorp.com :: 303.748.6894/c 303.448.7756/fx ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
