**
C. Belingeri, B. Germano**

##
On Appel-Type Quadrature Rules

**abstract:**

The Radon technique is applied in order to recover a quadrature rule based
on Appel polynomials and the so called Appel numbers. The relevant formula
generalizes both the Euler--MacLaurin quadrature rule and a similar rule using
Euler (instead of Bernoulli) numbers and even (instead of odd) derivatives of
the given function at the endpoints of the considered interval. In the general
case, the remainder term is expressed in terms of Appel numbers, and all
derivatives appear. A numerical example is also included.