How to show orthogonality of Hermite polynomials??? INTEGRATE from -inf to +inf the argument ( e^(-x^2) *H_n(x)*H_m(x) ) where H_n(x)=(-1)^n * e^(x^2) * d^(n) /(dx)^n (e^(-x^2))

Question

How to show orthogonality of Hermite polynomials???  INTEGRATE from -inf to +inf the argument ( e^(-x^2) *H_n(x)*H_m(x) )  where H_n(x)=(-1)^n * e^(x^2) * d^(n) /(dx)^n (e^(-x^2))

anonymous · Answer

Need a website showing an example of this

saifoo.khan · Answer

@satellite73

anonymous · Answer

the answer should be: 2^n * n! *SQRT(Pi) *DeltaFunction(mn)

anonymous · Answer

I can show it vanishes for n not = to m but I cant get the factor in front when n=m

hero · Answer

Is this graduate level mathematics question?

anonymous · Answer

Perhaps..... Im not a grad student though

anonymous · Answer

Its from a grad math methods class I'm taking.,.... I'm currently reading the Arken book to try and understand this Special functions stuff...

hero · Answer

Enjoy!