generating function
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.
Noun
- 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....
- 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...
- 2003, Sergei K. Lando (author & translator), Lectures on Generating Functions, American Mathematical Society.
Origin
The concept was introduced by French mathematician Abraham de Moivre in 1730.
Forms
Hypernyms
Hyponyms
exponential generating function Bell series Dirichlet series Lambert series ordinary generating function