Polynomial sequence

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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[edit]

Some 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]

See also[edit]

References[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 0-486-44129-3.
  • Williamson, S. Gill "Combinatorics for Computer Science", Dover Publications, (2002) p177.