Polynomial sequence: Difference between revisions

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{{Use American English|date = March 2019}}

In [[mathematics]], a '''polynomial sequence''' is a [[sequence]] of [[polynomial]]s indexed by the nonnegative integers 0, 1, 2, 3, ..., in which each [[indexed family|index]] is [[equality (mathematics)|equal]] to the degree of the corresponding polynomial. Polynomial sequences are a topic of interest in [[enumerative combinatorics]] and [[algebraic combinatorics]], as well as [[applied mathematics]].

{{Short description|Sequence valued in polynomials}}

In [[mathematics]], a '''polynomial sequence''' is a [[sequence]] of [[polynomial]]s indexed by the nonnegative integers[[integer]]s 0, 1, 2, 3, ..., in which each [[indexed family|index]] is [[equality (mathematics)|equal]] to the [[degree of a polynomial|degree]] of the corresponding polynomial. Polynomial sequences are a topic of interest in [[enumerative combinatorics]] and [[algebraic combinatorics]], as well as [[applied mathematics]].

==Examples==

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* [[Hermite polynomials]]

Many are studied in [[algebra]] and combinatorics:

* [[Monomial]]s

* [[Rising factorial]]s