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math121b:02-26 [2020/02/28 01:02] pzhou removed |
math121b:02-26 [2020/02/28 13:28] (current) pzhou [Rodrigue Formula] |
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Today we begin Chapter 12, the series solution to ODE. | Today we begin Chapter 12, the series solution to ODE. | ||
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===== Rodrigue Formula ===== | ===== Rodrigue Formula ===== | ||
- | $$ P_l(x) = \frac{1}{2 l!} (\d_x)^l (x^2 -1)^l $$ | + | $$ P_l(x) = \frac{1}{2^l l!} (\d_x)^l (x^2 -1)^l $$ |
Let's show that it satisfies the Legendre equation. | Let's show that it satisfies the Legendre equation. | ||
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