Explore relationships

Touchard polynomials

The Touchard polynomials, studied by Jacques Touchard (1956), also called the exponential polynomials or Bell polynomials, comprise a polynomial sequence of binomial type defined by Tn(x)=∑k=0nS(n,k)xk=∑k=0n{nk}xk,{\displaystyle T_{n}(x)=\sum _{k=0}^{n}S(n,k)x^{k}=\sum _{k=0}^{n}\left\{{n \atop k} ight\}x^{k},}where S(n,k)={nk}{\displaystyle S(n,k)=\left\{{n \atop k} ight\}} is a Stirling number of the second kind, i.e., the number of partitions of a set of size n into k disjoint non-empty subsets.

Use + to expand a branch. Click a topic name to open its summary.