Polynomial sequence
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 | It has been suggested that this article be merged into polynomial. (Discuss) Proposed since January 2008. |
In mathematics, a polynomial sequence is a sequence of polynomials indexed by the nonnegative integers 0, 1, 2, 3, ..., in which each index is equal to the degree of the corresponding polynomial. Polynomial sequences are a topic of interest in enumerative combinatorics and algebraic combinatorics.
Examples
- Monomials
- Rising factorials
- Falling factorials
- Abel polynomials
- Bell polynomials
- Bernoulli polynomials
- Chebyshev polynomials
- Dickson polynomials
- Fibonacci polynomials
- Hermite polynomials
- Legendre polynomials
- Laguerre polynomials
- Lucas polynomials
- Spread polynomials
- Touchard polynomials
- Rook polynomials
Classes of polynomial sequences
- Polynomial sequences of binomial type
- Orthogonal polynomials
- Secondary polynomials
- Sheffer sequence
- Sturm sequence
- Generalized Appell polynomials
References
- Aigner, Martin. "A course in enumeration" GTM Springer. (2007) p21
- Williamson, S. Gill "Combinatorics for Computer Science" Dover. (2002) p177