For each natural number $n$ there is a Gegenbauer polynomial of degree n, depending on a spectral parameter $\lambda$. They fulfill many recurrent relations. The question is how to recognize their factorization properties (employing recursive relations, say), i.e. for which value of the spectral parameter $\lambda$ and $n\geq m$, the degree $n$ Gegenbauer is divisible by degree $m$ Gegenbauer.
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