polynomial sequence
{{Use American English|date = March 2019}}
{{Short description|Sequence valued in polynomials}}
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:
Others come from statistics:
Many are studied in algebra and combinatorics:
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|978-0-486-44139-9}}.
- Williamson, S. Gill "Combinatorics for Computer Science", Dover Publications, (2002) p177.
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