linguistic:translation
Polynomial sequence generating functions

The idea of generating functions can be extended to sequences of other objects. Thus, for example, polynomial sequences of binomial type are generated by: e x f (t) = ∑ n = 0 ∞ p n (x) n ! t n {\displaystyle e^{xf(t)}=\sum _{n=0}^{\infty }{\frac {p_{n}(x)}{n!}}t^{n}} where p (x) is a sequence of polynomials and f (t) is a function of a certain form. Sheffer sequences are generated in a similar way. See the main article generalized Appell polynomials for more information.

Examples of polynomial sequences generated by more complex generating functions include: