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general solution for element of series

• To: mathgroup at smc.vnet.net
• Subject: [mg39914] general solution for element of series
• From: "Michael Beqq" <mbekkali at iastate.edu>
• Date: Tue, 11 Mar 2003 02:38:35 -0500 (EST)
• Organization: Iowa State University
• Sender: owner-wri-mathgroup at wolfram.com

Suppose I have expressions of x generated by some function f for any given
j:

(j=1) => z=1/x=H[x,1]
(j=2) => z=1/(x-(1/x))=H[x,2]
(j=3) => z=1/(x-(1/(x-(1/x))))=H[x,3]
(j=4) => z=1/(x-1/(x-(1/(x-(1/x)))))=H[x,4]
...........
(j=j) => z= H(x,j)

I would like to know how I can find the function that generates this
sequence for some particular element j, that is, for any j=1,....,J I can
express z as a function of x and j;  for example, if j=2 I would like to get
z=1/(x-(1/x)), while if j=3 I would like to get z=1/(x-(1/(x-(1/x)))).
There must be a way to do that, at least I hope so, because there exist
operators in Mathematica 4.0 (full version) that allow one to get any
element, z, of the sequence if one knows the generating function, f, and the
element's number, j (in short, I need to find the functional form of
H[x,j]).

I hope I was clear enough   :)

Please help. Michael Beqq

• Follow-Ups:
  • Re: general solution for element of series
    • From: Dr Bob <drbob@bigfoot.com>