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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

• Classes of polynomial sequences

• See also

• References

Some polynomial sequences arise in physics and approximation theory as the solutions of certain ordinary differential equations:

• Laguerre polynomials

• Chebyshev polynomials

• Legendre polynomials

• Jacobi polynomials

Others come from statistics:

• Hermite polynomials

Many are studied in algebra and combinatorics:

• Monomials

• Rising factorials

• Falling factorials

• All-one polynomials

• Abel polynomials

• Bell polynomials

• Bernoulli polynomials

• Cyclotomic polynomials

• Dickson polynomials

• Fibonacci polynomials

• Lagrange polynomials

• Lucas polynomials

• Spread polynomials

• Touchard polynomials

• Rook polynomials

• Polynomial sequences of binomial type

• Orthogonal polynomials

• Secondary polynomials

• Sheffer sequence

• Sturm sequence

• Generalized Appell polynomials

• Umbral calculus

• 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.