(a) Show that if =2k+1, any solution of Hermites ODE is a
Chapter 9, Problem 7(choose chapter or problem)
(a) Show that if =2k+1, any solution of Hermites ODE is a power series but not a polynomial. (b) DeducethatinthiscasenosolutionofHermitesODEcansatisfythe conditionatinnity.(Hint:Usetherecursionrelation(18)tondthe behaviorof ak as k.Comparewiththepowerseriesexpansion of ex2. Deduce that u(x, t) behaves like ex2 as|x|.)
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