  An explicit structure relation for Askey-Wilson polynomials is given. This
involves a divided q-difference operator which is skew symmetric with respect
to the Askey-Wilson inner product and which sends polynomials of degree n to
polynomials of degree n+1. By specialization of parameters and by taking
limits, similar structure relations, as well as lowering and raising relations,
can be obtained for other families in the q-Askey scheme and the Askey scheme.
This is explicitly discussed for Jacobi polynomials, continuous q-Jacobi
polynomials, continuous q-ultraspherical polynomials, and for big q-Jacobi
polynomials. An already known structure relation for this last family can be
obtained from the new structure relation by using the three-term recurence
relation and the second order q-difference formula. The results are also put in
the framework of a more general theory. Their relationship with earlier work by
Zhedanov and Bangerezako is discussed. There is also a connection with the
string equation in discrete matrix models and with the Sklyanin algebra.
