Orthonormal hermite polynomials

Question

Assignment:

Knowing that {H_n}, n = 0, 1, 2... are orthogonal and

(H_o, H_o) = √π, (H_n, H_n) = 2n(H_n-1, H_n-1), n ∈ N

with respect to a suitable weight function p(x), write down first two orthonormal Hermite polynomials.

Provide complete and step by step solution for the question and show calculations and use formulas.