Basic algebraic identities
- To: mathgroup at smc.vnet.net
- Subject: [mg87809] Basic algebraic identities
- From: Boris Blankleider <boris.blankleider at flinders.edu.au>
- Date: Thu, 17 Apr 2008 06:59:28 -0400 (EDT)
1. Which basic algebraic identities does Mathematica know? For
example, it does not appear to know the orthogonality relation for
Legendre polynomials:
Integrate[ LegendreP[m, x] LegendreP[n, x], {x,-1,1}] - 2/(2 n+1)
KroneckerDelta[n,m] = 0
When I try this out, I find that the left hand side does not evaluate
to zero - even if I add assumptions about n & m being positive
integers. Yet a similar check shows that it does know about
Cos[x]^2 + Sin[x]^2] - 1 = 0
(although one does need to use Simplify[%] before it reveals its
knowledge).
2. If it really does not know the orthogonality relation for Legendre
polys, how would I teach it?