Appell Polynomial

A type of Polynomial which includes the Bernoulli Polynomial, Hermite Polynomial, and Laguerre Polynomial as special cases. The series of Polynomials $\{A_n(z)\}^\infty_{n=0}$ is defined by

$$A(t)e^{zt}=\sum_{n=0}^\infty A_n(z)t^n,$$

where

$$A(t)=\sum_{k=0}^\infty a_kt^k$$

is a formal Power series with $k=0$, 1, ...and $a_0\not=0$.

References

Hazewinkel, M. (Managing Ed.). Encyclopaedia of Mathematics: An Updated and Annotated Translation of the Soviet ``Mathematical Encyclopaedia.'' Dordrecht, Netherlands: Reidel, pp. 209-210, 1988.