       Re: general solution for element of series

• To: mathgroup at smc.vnet.net
• Subject: [mg39991] Re: general solution for element of series
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Fri, 14 Mar 2003 04:45:21 -0500 (EST)
• Organization: The University of Western Australia
• References: <b4k3uo\$8hn\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```In article <b4k3uo\$8hn\$1 at smc.vnet.net>,
"Michael Beqq" <mbekkali at iastate.edu> wrote:

> 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;

Since it is a continued fraction, you can use

H[x_,j_]:=FromContinuedFraction[Join[{0}, Table[(-1)^i x, {i, 0, j-1}]]]

Cheers,
Paul

--
Paul Abbott                                   Phone: +61 8 9380 2734
School of Physics, M013                         Fax: +61 8 9380 1014
The University of Western Australia      (CRICOS Provider No 00126G)
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Crawley WA 6009                      mailto:paul at physics.uwa.edu.au
AUSTRALIA                            http://physics.uwa.edu.au/~paul

```

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