Unformatted text preview: ˙ r = sin r ˙ θ =-1 Are there any non-trivial periodic solutions? If yes, are they limit cycles? If there are non-trivial 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 n-1 ( 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
- Recurrence relation, AirTrain Newark, linearly independent solutions, Patrick De Leenheer