Generalized Appell polynomials

Generalized Appell polynomials are a family of orthogonal polynomials that generalize the classical Appell polynomials. Appell polynomials are a set of polynomials \(A_n(x)\) such that the \(n\)-th polynomial can be defined via a generating function or a differential equation relationship. Specifically, Appell polynomials satisfy the condition: \[ A_n'(x) = n A_{n-1}(x) \] with a given initial condition.