Meaning of generating function | Babel Free

Definitions

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.

Equivalents

Examples

“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.”

“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.”

“2003, Sergei K. Lando (author & translator), Lectures on Generating Functions, American Mathematical Society.”

CEFR level