Generating function for Laguerre L
From specialfunctionswiki
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
- 1968: W.W. Bell: Special Functions for Scientists and Engineers ... (previous) ... (next): Theorem 6.1
