If $f_0(x)=1$, and $f_{n+1}=\frac{d}{dx}((x^2-1)f_n(x))$, prove that every $f_n$ has exactly $n$ distinct zeroes, all located in the interval $(-1,1)$. It's got me stumped, so any help/pointers would be appreciated.
2026-04-12 09:33:16.1775986396
How to identify properties of the zeroes of this polynomial?
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