I forgot that there is a J Wiki essay on this topic: http://www.jsoftware.com/jwiki/Essays/Continued_Fractions
On Sun, Feb 23, 2014 at 4:03 PM, Roger Hui <rogerhui.can...@gmail.com>wrote: > Sometimes %`+/ and %`+/\ are the expressions, depending on circumstances. > For example: > > x=: ?. 0 > x > 0.038363 > %`+/ x,,(1+2*i.20),.*:x > 0.0383442 > 7 o. x > 0.0383442 > > Gauss, 1812, according to C.D. Olds, Continued Fractions, MAA, 1963. > > > > > On Sun, Feb 23, 2014 at 3:55 PM, Roger Hui <rogerhui.can...@gmail.com>wrote: > >> +`%/ and +`%/\ are the expressions you seek. For example: >> >> +`%/3,20$4 6 >> 3.60555 >> %: 13 >> 3.60555 >> >> >> >> >> On Sun, Feb 23, 2014 at 2:17 PM, km <k...@math.uh.edu> wrote: >> >>> The generalized continued fraction >>> >>> b0 + a1 >>> --------- >>> b1 + a2 >>> --------- >>> b2 + a3 >>> -------- >>> b3 + ... >>> >>> is the infinite sequence >>> >>> b0 , b0 + a1%b1 , b0 + a1%b1 + a2%b2 , b0 + a1%b1 + a2%b2 + a3%b3 , ... >>> >>> where between the commas I am assuming J's right-to-left evaluation. >>> The nth term would be >>> >>> b0 + a1%b1 + a2%b2 + a3%b3 + ... + an%bn (still using right to left >>> evaluation). >>> >>> What is a good way to calculate this nth term in J? >>> >>> >>> For a half-page introduction to generalized continued fractions see >>> >>> http://people.math.sfu.ca/~cbm/aands/page_19.htm >>> >>> Continued fractions for ln(1+z) and ln((1+z)%(1-z)) are given here >>> >>> http://people.math.sfu.ca/~cbm/aands/page_68.htm >>> >>> >>> --Kip Murray >>> >>> Sent from my iPad >>> >>> ---------------------------------------------------------------------- >>> For information about J forums see http://www.jsoftware.com/forums.htm >>> >> >> > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
