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Closed form for $\sum_{j=0}^{\infty}{\alpha \choose j} {\beta \choose j}x^j$
As stated, I wonder if there is a closed form for the generating function $F_{\alpha,\beta}(x):=\sum_{j=0}^{\infty}{\alpha \choose j} {\beta \choose j}x^j$ where $\alpha,\beta \in\mathbb{N}$. Calling ...
