Editing Probability-generating function (section)

=== Multivariate case ===
If {{math|1=''X'' = (''X''<sub>1</sub>,...,''X<sub>d</sub>'')}} is a discrete random variable taking values {{math|(''x''<sub>1</sub>, ..., ''x<sub>d</sub>'')}} in the {{mvar|d}}-dimensional non-negative [[integer lattice]] {{math|{0,1, ...}<sup>''d''</sup>}}, then the ''probability generating function'' of {{math|''X''}} is defined as
<math display="block">G(z) = G(z_1,\ldots,z_d) = \operatorname{E}\bigl (z_1^{X_1}\cdots z_d^{X_d}\bigr) = \sum_{x_1,\ldots,x_d=0}^{\infty}p(x_1,\ldots,x_d) z_1^{x_1} \cdots z_d^{x_d},</math>
where {{mvar|p}} is the probability mass function of {{mvar|X}}. The power series converges absolutely at least for all complex vectors <math>z = (z_1, ... z_d) \isin \mathbb{C}^d</math> with <math>\text{max}\{|z_1|, ..., |z_d|\} \le 1.</math>