formal power series
Noun
Meaning
formal power series (plural formal power series)
(mathematics, algebra) Any finite or infinite series of the form
a
0
+
a
1
x
+
a
2
x
2
⋯
=
∑
i
a
i
x
i
{\displaystyle \textstyle a_{0}+a_{1}x+a_{2}x^{2}\dots =\sum _{i}{a_{i}x^{i}}}
, where the ai are numbers, but it is understood that no value is assigned to x.
Examples
Applications Formal power series can be used to solve recurrences occurring in number theory and combinatorics.
Power series main Formal power series are like polynomials, but allow infinitely many non-zero terms to occur, so that they do not have finite degree.