Editing Probability-generating function (section)

===Power series===

Probability generating functions obey all the rules of power series with non-negative coefficients.  In particular, <math>G(1^-) = 1</math>, where <math>G(1^-) = \lim_{x\to 1, x<1} G(x)</math>, [[One-sided limit|x approaching 1 from below]], since the probabilities must sum to one. So the [[radius of convergence]] of any probability generating function must be at least 1, by [[Abel's theorem]] for power series with non-negative coefficients.