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