Hi all, the title pretty much says it all. Does anyone know the generating functions for multi-dimensional Chebyshev Polynomials? Does that question even make sense?
I'm a physicists and I'm the first to admit my maths skills are not as good as they should be. I use Chebyshev Polynomials from time to time as arbitrary fitting functions, i.e. by numerically searching for the co-efficients of the first N Chebyshev's to best fit some unknown function to data. However I want to generalise this to multi-dimensional problems, but I can't see an obvious unique way to do this. I don't really know how to derive the 1D case (I just read the generating function out of a textbook...) so I don't know it it even makes sense to speak of them as functions of more than one variable?
Any advice or feedback would be appreciated.