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Unformatted text preview: r = sin r =1 Are there any nontrivial periodic solutions? If yes, are they limit cycles? If there are nontrivial periodic solutions, how many are there, and what can be said about their stability? 5. The Legendre polynomials P n ( x ) satisfy the following recurrence relation: ( n + 1) P n +1 ( x ) = (2 n + 1) xP n ( x )nP n1 ( x ) . Given that P ( x ) = 1 and P 1 ( x ) = x , determine P 2 ( x ), P 3 ( x ) and P 4 ( x ). * Instructor: Patrick De Leenheer....
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This note was uploaded on 04/07/2008 for the course MAP 4305 taught by Professor Deleenheer during the Spring '06 term at University of Florida.
 Spring '06
 DeLeenheer

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