= Generating function for Laguerre polynomials
{title2=$\sum_{n=0}^\infty L_n(x)h^n=(1-h)^{-1}e^{-xh/(1-h)}$}
The <generating function> holds for $|h|<1$ and fixed $x$. From <Rodrigues' formula>, $L_n(x)=\sum_{j=0}^n\binom nj(-x)^j/j!$. Sum first over $n\geq j$, using $\sum_{n\geq j}\binom njh^n=h^j/(1-h)^{j+1}$, and then over $j$ to obtain the <exponential function>. The absolute-value double series is finite for $|h|<1$, justifying the rearrangement. Alternatively, the weighted <inner product> and the <Laplace transform of a Laguerre polynomial> extract the coefficient $h^n$.
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