Re: Function of function analytic definition

• To: mathgroup at smc.vnet.net
• Subject: [mg66226] Re: [mg66148] Function of function analytic definition
• From: "Ingolf Dahl" <ingolf.dahl at telia.com>
• Date: Thu, 4 May 2006 05:21:37 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Narasimham,
See http://en.wikipedia.org/wiki/Fa%C3%A0_di_Bruno%27s_formula
History of Faà di Bruno's Formula
(http://www.maa.org/news/monthly217-234.pdf).
Plug this formula into the general Taylor expansion!
Hope that helps!

Best regards
Ingolf Dahl
Sweden

> -----Original Message-----
> From: Narasimham [mailto:mathma18 at hotmail.com]
To: mathgroup at smc.vnet.net
> Sent: den 1 maj 2006 07:31
> To: mathgroup at smc.vnet.net
> Subject: [mg66226] [mg66148] Function of function analytic definition
>
> 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.
>

```

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