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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 dierential equation xy + y + xy = 0 . 1 2 7. Let y = f ( x ) be a solution of the diFerential equation x 2 dy dx-xy = sin x, with initial condition f (0) = c . ind a power series expansion for f near x = 0. 8. or what values of and does i dx x + x converge?...
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This note was uploaded on 12/27/2011 for the course MATH 118c taught by Professor Garcia during the Fall '09 term at UCSB.
- Fall '09