Polynomial sequence

From Exampleproblems

Definition

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
• Touchard polynomials

See also

• Polynomial sequences of binomial type
• Orthogonal polynomials
• Sheffer sequence