Function of function analytic definition

*To*: mathgroup at smc.vnet.net*Subject*: [mg66148] Function of function analytic definition*From*: "Narasimham" <mathma18 at hotmail.com>*Date*: Mon, 1 May 2006 01:30:33 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Is there perhaps a mixed functional relation between 'n' th term of Taylor's Series for f(x0 + h) = f '(n-1)(x0)/(n-1)! and the same for g(x0 + h) = g '(n-1)(x0)/(n-1)! to obtain/ evaluate 'n' th term of f( g(x) ) and g( f(x) )? Is it not possible by using Jacobian criteria using multi-parameter function definitions available on Mathematica to find this out? [Subject to of course assumption of existence, uniqueness, smoothness and other well ordered analytic functional behaviors of f and g]. Hoping for any related comments. Somehow this comes to me often, earlier queries did not help clear this up. Regards.