[yaser]

Originally Posted by skwong

In lect 12, we learn the regularization for a nonlinear transformation which is
composed of Legendre polynomials. But then in hw6, Q2 to Q6,
The nonlinear transform doesn't talk anything about Legendre polynomials.

Does it mean, Legendre polynomials is used in deriving the theory,
and any function, including the in hw6, can actually be
expressed in terms of Legendre polynomials ? Further, does it only hold true
for the range -1 to 1 ?

Any polynomial, including the one in HW 6, can be expressed in terms Legendre polynomials. The polynomial can be defined outside the range but the orthognality of Legendre polynomials is within .