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polynomial sequence
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:
* 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
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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