A couple notes here: One is that 0j18":Y will give you 18 places after the decimal point regardless of the magnitude of Y
Another is that we can inspect intermediate results in the expression %-/%!2+x:i.x Let's try that here with smaller values for x (and leaving out the x: so that we're using floating point approximations for more comfortable display): i.4 0 1 2 3 !i.4 1 1 2 6 !2+i.4 2 6 24 120 %!2+i.4 0.5 0.166667 0.0416667 0.00833333 %~/%!2+i.4 2.4 Inspecting these results (and perhaps playing with a few other examples), I am reminded that !0 and !1 both have the value 1. And, of course, the reciprocal of 1 is 1. And, %~ will finish up by dividing the accumulated result by these values. So, this skips a couple unnecessary "divide by 1" steps. But, also, adding 2 means that we've added another two significant terms to the initial (right hand side) part of the series, giving us a more accurate result. These correspond to relatively small values in the result, but they do increase its precision. And, I do see a change there, on the right hand side, in the case of the example you suggested: 0j18":%-/%!2+i.x:10 2.718281842777827338 0j18":%-/%!i.x:10 2.718283693893449991 I hope this helps, -- Raul On Tue, Oct 3, 2023 at 3:26 AM Richard Donovan <rsdono...@hotmail.com> wrote: > > After watching a math video on YouTube I started to investigate the > implementation of alternating sequences in J. > > Using the site search function, (alternating sequences site:jsoftware.com) I > discovered an entry in the NYCJUG of 2022-11-08 which contains an excellent > example: > > > calce=: 13 : '%-/%!2+i.x: y' > calce 10 > 3991680r1468457 > 20j18":calce 10 NB. Format rational to 20-digit decimal with 18 > places past the decimal > 2.718281842777827338 > > Using this as a startpoint, I followed the logic thru but couldn't understand > why 2 is added to i. x: y > > Removing the 2+ doesn't seem to affect the result in any of the cases I tried. > > > Thanks in advance, > > Richard > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
