A classic 1970 paper of B. Muckenhoupt established necessary and sufficient conditions for weighted L(p) convergence of Hermite series, that is, orthogonal expansions corresponding to the Hermite weight. We generalize these to orthogonal expansions for a class of Freud weights W-2 := e(-2Q), by first proving a bound for the difference of the orthonormal polynomials of degree n + 1 and n - 1 of the weight W-2. Our identical necessary and sufficient conditions close a slight gap in Muckenhoupt's conditions for the Hermite weight at least for p > 1. Moreover, our necessary conditions apply when Q(x) = \x\(alpha), alpha > 1, while our sufficient conditions apply at least for alpha = 2, 4, 6,....
