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
editSome 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
edit- Polynomial sequences of binomial type
- Orthogonal polynomials
- Secondary polynomials
- Sheffer sequence
- Sturm sequence
- Generalized Appell polynomials
See also
editReferences
edit- 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.