[Jprogramming] Approximating e

[EelVex]

* Summing infinite series

   +/%!i.100x
   +/^ t. i.100x  NB. Taylor coefficients
%+/((_1&^)%!)i.100x
etc

* Taking an asymptotic

(-^~1-%) 100x
((^~%~^~@>:) - (^~%^~@<:))100x
etc

* Continued fractions

   +`%/2 1,2#>:i.100x
   +`%/2, 2#2+i.100x
   (+%)/2 1, ,(1 1,~])"0 +:>:i.100x   NB. canonical form




On Mon, Mar 10, 2014 at 6:38 PM, km <km at math.uh.edu> wrote:

> The rational  2721r1001  approximates  e  to six, almost seven decimal
> places:
>
>     0j7 ": (^ 1) ,: 2721r1001
>  2.7182818
>  2.7182817
>
> I got 2721r1001 from a continued fraction.  How would you look for
> rational approximations to  e  ?
>
> --Kip Murray
>
> Sent from my iPad
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