Generating function for Laguerre L

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Theorem

The following formula holds: $$\dfrac{e^{\frac{-xt}{1-t}}}{1-t} = \displaystyle\sum_{k=0}^{\infty} L_k(x)t^k,$$ where $e^{\frac{-xt}{1-t}}$ denotes an exponential function and $L_k$ denotes Laguerre L.

Proof

References