cv=: ([: (+`%/) 1 }.,)\@|: I hope this helps...
-- Raul On Sat, Mar 12, 2016 at 1:21 PM, Kip Murray <[email protected]> wrote: > Here you go: > > nume =: 1 , 1 % 4x * _1 + 4 * [: *:@>:@i. <: > > dene =: 1 1r2 , 1 $~ _2 + ] > > I think I got those from Abramowitz and Stegun. > > (_1 , nume 6),: dene 7 > _1 1 1r12 1r60 1r140 1r252 1r396 > 1 1r2 1 1 1 1 1 > > --Kip > > > On Saturday, March 12, 2016, Raul Miller <[email protected]> wrote: > >> How do you compute the first two rows? >> >> Thanks, >> >> -- >> Raul >> >> On Saturday, March 12, 2016, Kip Murray <[email protected] >> <javascript:;>> wrote: >> >> > The challenge is at the end. First a table for a finite continued >> fraction >> > that approximates e =: ^ 1 . >> > --Kip Murray >> > >> > >> > The table below summarizes a finite continued fraction which begins >> > >> > 1 >> > 1 + ------------- >> > 1r12 >> > 1r2 + -------- >> > 1r60 >> > 1 + ------ >> > >> > 1 + . >> > . >> > . >> > >> > table >> > _1 1 1r12 1r60 1r140 1r252 1r396 >> > 1 1r2 1 1 1 1 1 >> > 1 3 19r7 193r71 2721r1001 49171r18089 1084483r398959 >> > >> > >> > You must ignore the _1 in the upper left corner. You see how the first >> row >> > identifies numerators and the second row numbers on the "diagonal" of the >> > continued fraction. >> > >> > >> > The third row gives the "convergents", results of terminating the >> continued >> > fraction at a diagonal number. The first four convergents are >> > >> > 1 , (1 + 1 % 1r2) , (1 + 1 % 1r2 + 1r12 % 1) , (1 + 1 % 1r2 + 1r12 % 1 + >> > 1r60 % 1) >> > >> > >> > The convergents of this continued fraction approximate the number e =: >> ^ 1 >> > . >> > >> > 2 * 0.5 * {: table >> > 1 3 2.714285714 2.718309859 2.718281718 2.718281829 2.718281828 >> > >> > >> > Now, how would you write verb cv which provides the third row of the >> table >> > given the first two? >> > >> > 2 {. table >> > _1 1 1r12 1r60 1r140 1r252 1r396 >> > 1 1r2 1 1 1 1 1 >> > >> > cv 2 {. table >> > 1 3 19r7 193r71 2721r1001 49171r18089 1084483r398959 >> > >> > >> > --Kip Murray >> > >> > >> > >> > -- >> > Sent from Gmail Mobile >> > ---------------------------------------------------------------------- >> > For information about J forums see http://www.jsoftware.com/forums.htm >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm > > > > -- > Sent from Gmail Mobile > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
