[Jprogramming] Generalized continued fractions

[Pascal Jasmin]

a1n =. i.5
b1n =. >: i.5
b0 =. 1

  1 + +/(i.5) % (>: i.5)
3.71667



----- Original Message -----
From: km <km at math.uh.edu>
To: "programming at jsoftware.com" <programming at jsoftware.com>
Cc: 
Sent: Sunday, February 23, 2014 5:17:36 PM
Subject: [Jprogramming] Generalized continued fractions

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