Editing Generating function (section)

==== Multivariate case ====
Multivariate generating functions arise in practice when calculating the number of [[contingency tables]] of non-negative integers with specified row and column totals. Suppose the table has {{mvar|r}} rows and {{mvar|c}} columns; the row sums are {{math|''t''<sub>1</sub>, ''t''<sub>2</sub> ... ''t<sub>r</sub>''}} and the column sums are {{math|''s''<sub>1</sub>, ''s''<sub>2</sub> ... ''s<sub>c</sub>''}}. Then, according to [[I. J. Good]],<ref name="Good 1986">{{cite journal |last=Good |first=I. J. |year=1986 |title=On applications of symmetric Dirichlet distributions and their mixtures to contingency tables |journal=[[Annals of Statistics]] |volume=4 |issue=6 |pages=1159–1189 |doi=10.1214/aos/1176343649 |doi-access=free}}</ref> the number of such tables is the coefficient of:
<math display="block">x_1^{t_1}\cdots x_r^{t_r}y_1^{s_1}\cdots y_c^{s_c}</math>in:<math display="block">\prod_{i=1}^{r}\prod_{j=1}^c\frac{1}{1-x_iy_j}.</math>