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
Some polynomial sequences arise in physics and approximation theory as the solutions of certain ordinary differential equations:
Other come from statistics:
Many are studied in algebra and combinatorics:
- Monomials
- Rising factorials
- Falling factorials
- Abel polynomials
- Bell polynomials
- Bernoulli polynomials
- Dickson polynomials
- Fibonacci 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.