Does Transforming Hermite Polynomials Affect Their Orthogonality?

[Frank Einstein]

Hello everyone.

I am working with generalized polynomial chaos. To represent a Normal random variable, the Hermite polynomials are used. However, as far as I understand, these represent N(0,1); if what I have read is correct, if I want to work with any other mean and variance, I shoud simply use the fact that Z=(X-μ)/σ and find the new polynomials (X) substituting the regular ones (Z), which would be: 1, Z, (Z²-1)... which would mean that X₁= σZ-μ and X₂=σ(Z²-1)-μ...

Can someone please tell me if I am right?

Thanks.

 

[fresh_42]

I think you are, but it would be interesting to know how the chaos functions react to coordinate transformations.

 

[Fred Wright]

Does your transformation preserve orthogonality? I would think that the requirement of orthogonality would demand zero mean...i.e. for $i\neq j$$$<\Psi_i \Psi_j>=0$$