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Unformatted text preview: , R ]. 6. The Bessel function of zero order may be deFned by J ( x ) = ∞ s n =0 (1) n x 2 n 4 n ( n !) 2 . ±ind its radius of convergence, and show that J is a solution of the di²erential equation xy ′′ + y ′ + xy = 0 . 1 2 7. Let y = f ( x ) be a solution of the diFerential equation x 2 dy dxxy = sin x, with initial condition f (0) = c . ±ind a power series expansion for f near x = 0. 8. ±or what values of α and β does i ∞ dx x α + x β converge?...
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 Fall '09
 Garcia
 Math, Power Series, nan xn−1, convergence R. Prove

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