MathGroup Archive 2008

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Basic algebraic identities


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?




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