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
