Polynomial sequence

Summary

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:

Others come from statistics:

Many are studied in algebra and combinatorics:

Classes of polynomial sequences

See also

References

  • 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.