(a) Laguerre's differential equation ty" + (1 - t)y' + ny = 0 is known to possess
Chapter 4, Problem 65(choose chapter or problem)
(a) Laguerre's differential equation ty" + (1 - t)y' + ny = 0 is known to possess polynomial solutions when n is a nonnegative integer. These solutions are naturally called Laguerre polynomials and are denoted by Lit). Find y = Lit), for n = 0, 1, 2, 3, 4 if it is known that LiO) = 1. (b) Show that where Y(s) = s; {y} and y =Lit) is a polynomial solution of the DE in part (a). Conclude that - et d n n -t Lit) - ----,-d n t e , n = 0, 1, 2, ....
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