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
> > ----------------------------------------------------------------------
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> ----------------------------------------------------------------------
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