In mathematics, a polynomial sequence { p n } {\displaystyle \{p_{n}\}} has a generalized Appell representation if the generating function for the polynomials takes on a certain form: K = A Ψ = ∑ n = 0 ∞ p n w n {\displaystyle K=A\Psi =\sum _{n=0}^{\infty }p_{n}w^{n}} where the generating function or kernel K {\displaystyle K} is composed of the series A = ∑ n = 0 ∞ a n w n {\displaystyle A=\sum _{n=0}^{\infty }a_{n}w^{n}\quad } with a 0 ≠ 0 {\displaystyle a_{0}\neq 0} and Ψ = ∑ n = 0 ∞ Ψ n t n {\displaystyle \Psi =\sum _{n=0}^{\infty }\Psi _{n}t^{n}\quad } and all Ψ n ≠ 0 {\displaystyle \Psi _{n}\neq 0} and g = ∑ n = 1 ∞ g n w n {\displaystyle g=\sum _{n=1}^{\infty }g_{n}w^{n}\quad } with g 1 ≠ 0. Wikipedia