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. Various special polynomial sequences are known by eponyms; among these are:

Examples

• Monomials
• Rising factorials
• Falling factorials
• Abel polynomials
• Bell polynomials
• Bernoulli polynomials
• Chebyshev polynomials
• Fibonacci polynomials
• Hermite polynomials
• Legendre polynomials
• Laguerre 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