11. The Hermite polynomials, H„(x), satisfy the following: į. < Hn, Hm >= L e-x*Hn(x)Hm(x) dx = VT2"n! 8n,m: т ii. H,(x) = 2nHn-1(x). п-1 ii. Нn+1 (x) %3D 2хН, (х) — 2nНm-1 (х). iv. H„(x) = (-1)"e* (e-x*). Using these, show: a. H – 2xH + 2nHn = 0 [use properties ii. And iii. ]

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