Appell sequence

The Appell sequence refers to a specific type of polynomial sequence that is defined through a recurrence relation involving derivatives. It is most commonly associated with the Appell polynomials, which are a set of orthogonal polynomials related to the concept of generating functions. In general, an Appell sequence \( \{ P_n(x) \} \) is defined by the following properties: 1. **Polynomial Nature**: Each \( P_n(x) \) is a polynomial of degree \( n \).