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) 35 Stirling Highway Crawley WA 6009 mailto:paul at physics.uwa.edu.au AUSTRALIA http://physics.uwa.edu.au/~paul