*To*: mathgroup@smc.vnet.net*Subject*: [mg10323] writing out a general n-th order iterative eqn.*From*: ngrjn@u.washington.edu (V. Nagarajan)*Date*: Thu, 8 Jan 1998 23:40:48 -0500*Organization*: University of Washington, Seattle

I would appreciate someone pointing me in the right direction. I have an n-th order eqn., {rho^(n) (t)}ij = {A(t)}ij (x) {B(t).rho^(n-1) - rho^(n-1).B(t)}ij ^ = superscript {..}ij = ij-th matrix element . = scalar multiplication The equation gets quite tedious upon substituting for the lower order successively because {x.y}ij = Sum(k=1,N)({x}ik.{y}kl). For N=2 and n=3, i can express rho^(3) as a function of rho^(0) fairly easily. It is when these integers get to be larger, the bookkeeping gets to be horrendous. I am looking to use Mathematica, if possible, to express higher order rho as a function of rho^(0). It seems to me that since the equation can be iterated methodically, I should be able to use the symbolic aspect of Mathematica to write out all the terms. I have looked into the function Nest, but the convolution makes its application not straightforward at the least. Where can i find out more? Thanks in advance for all info. - Nagarajan