[Jprogramming] Generalized continued fractions

[Pascal Jasmin]

I think the spec calls for different lists of a and b?


----- Original Message -----
From: Lizanets Danylo <iamweasel at ukr.net>
To: programming at jsoftware.com
Cc: "programming at jsoftware.com" <programming at jsoftware.com>
Sent: Sunday, February 23, 2014 5:55:29 PM
Subject: Re: [Jprogramming] Generalized continued fractions

Use (+%)/  
   (+%)/\9$1 
1 2 1.5 1.66667 1.6 1.625 1.61538 1.61905 1.61765 

--- Original message --- 
From: "km" < km at math.uh.edu > 
Date: 24 February 2014, 00:17:52 

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

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