Integer-parameter Laguerre contour residues
= Integer-parameter Laguerre contour residues
{c}
For $\lambda=N\geq0$, the amplitude $(t-1)^N/t^{N+1}$ has a pole at zero whose contour residue is a degree-$N$ Laguerre polynomial in $z$. For $\lambda=-m<0$, the amplitude $t^{m-1}/(t-1)^m$ has a pole at one whose residue is $e^z$ times a polynomial of degree $m-1$.