Unformatted text preview: ˙ r = sin r ˙ θ =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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 Spring '06
 DeLeenheer
 Recurrence relation, AirTrain Newark, linearly independent solutions, Patrick De Leenheer

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