Polynomial sequence
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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, as well as applied mathematics.
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
See Also
References
- Aigner, Martin. "A course in enumeration", GTM Springer, 2007, ISBN 3-540-39032-4 p21.
- Roman, Steven "The Umbral Calculus", Dover Publications, 2005, ISBN 0-486-44129-3.
- Williamson, S. Gill "Combinatorics for Computer Science", Dover Publications, (2002) p177.