Generating function for Laguerre L

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.

References

• 1968: W.W. Bell: Special Functions for Scientists and Engineers ... (previous) ... [[L n(x)=(e^x/n!)d^n/dx^n [x^n e^(-x)]|(next)]]: Theorem 6.1