d The Hermite polynomials are very important in physics. [See Wikipedia!] They are given by the expression H.(x) =(-1)"e** for n=0,1,2,... dar Fact: H, is a solution of the differential equation (e-*y)' + 2ne- y = 0. The first few are H, (t) = 1, H.(I) = 26, H, (x) = 4.r - 2, and Hz(t) = 873 120. Find the Fourier-Hermite series of the polynomial p(x) = ?X + 5x + 3 three ways: a. by integrating and using orthogonality. Note: [4.(-)?e* dr = V. 2"n! b. by inverting a certain matrix, c. by doing it an even easier way: just figuring out what the coefficients must be by common sense and simple algebra. d The Hermite polynomials are very important in physics. [See Wikipedia!] They are given by the expression H.(x) =(-1)"e** for n=0,1,2,... dar Fact: H, is a solution of the differential equation (e-*y)' + 2ne- y = 0. The first few are H, (t) = 1, H.(I) = 26, H, (x) = 4.r - 2, and Hz(t) = 873 120. Find the Fourier-Hermite series of the polynomial p(x) = ?X + 5x + 3 three ways: a. by integrating and using orthogonality. Note: [4.(-)?e* dr = V. 2"n! b. by inverting a certain matrix, c. by doing it an even easier way: just figuring out what the coefficients must be by common sense and simple algebra