I am trying to find sum of this series,
$$\sum_{k=0}^{\gamma} \binom{\gamma}{k} L_n^{a + k}(x) L_{c + k}^{b - k}(x).$$
Ideas/clues are welcome.
2026-04-14 03:28:01.1776137281
Laguerre Polynomial Series
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can you use this $\sum_{k=0}^{\gamma} \binom{\gamma}{k}L_{m + k}^{\alpha - k}(x) = L_{m+\gamma}^{\alpha}(x)$ and $\sum_{k=0}^{\gamma}L_k^{\alpha}(x) = L_{\gamma}^{\alpha+1}(x) $ ??