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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.