generating function

Noun

generating function (plural generating functions)

1. A formal power series with one indeterminate, whose coefficients encode a sequence that can be studied by algebraic manipulation of the series; any one of several generalizations, such as to encode more than one sequence or use more than one indeterminate.
   • A generating function is a device somewhat similar to a bag. Instead of carrying many little objects detachedly, which could be embarrassing, we put them all in a bag, and then we have only one object to carry, the bag.1954, George Pólya, Mathematics and Plausible Reasoning, Volume 1: Induction and Analogy in Mathematics, Princeton University Press, page 101
   • Most often generating functions arise from recurrence formulas. Sometimes, however, from a generating function you will find a new recurrence formula, not the one you started with, that gives new insights into the nature of your sequence.1990, Herbert S. Wilf, generatingfunctionology, Academic Press, page 2