Homepage › Solution manuals › Gilbert Strang › Linear Algebra and Learning from Data › Exercise 5.3.1
$G(z) = E[z^x] = ∑ z^np_n = ∑ z^ne^{−λ}λn n! = e^{−λ}∑ (zλ)n n! = e{-λ}e{zλ} = e^{(z − 1)λ}$