Recursive Proofs...

• To: mathgroup at smc.vnet.net
• Subject: [mg29890] Recursive Proofs...
• From: "Louis Trichard" <trich-lg at ee.usyd.edu.au>
• Date: Tue, 17 Jul 2001 01:00:35 -0400 (EDT)
• Organization: The University of Sydney, Australia
• Sender: owner-wri-mathgroup at wolfram.com

```Dear All,

I have a complicated 2d recursion in which I'd like to prove that the
r(i,i) = a^i. (i.e. something simple) by induction. I've left out the
definition of the recursive function, since it is not necessary.

I can use mathematica to show this simple expression for i = 1..100 or
more, i.e. Simplify[r[10,10]] = a^10, but this is no proof.

I would like some general advice on:
1/ How could one use mathematica to help prove such recursive
expressions by induction (or other methods) for general i, i.e. I know one
cannot use Simplify[r[i,i]], since this would give an infinite recursion
depth error.

Thanks for all your help,

Louis Trichard

```

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