Two expansion formulas involving the Rogers–Szegő polynomials with applications

Using two expansion formulas for the Rogers–Szegő polynomials and the Stieltjes–Wigert polynomials, we give new proofs of a variety of important classical formulas including Bailey's 6ψ6 summation, the Askey–Wilson integral and its extension. Furthermore, we give nontrivial extensions of the Andrews multiple version of the Rogers–Selberg identity, as well as the Sylvester identity.

Fault-Tolerant Protocols Using Single- and Multiple-Version Software Fault-Tolerance

This chapter discusses two large classes of fault-tolerance protocols: • Single-version protocols, that is, methods that use a non-distributed, single task provision, running side-by-side with the functional software, often available in the form of a library and a run-time executive. • Multiple-version protocols, which are methods that use actively a form of redundancy, as explained in what follows. In particular recovery blocks and N-version programming will be discussed. The two families have been grouped together in this chapter because of the several similarities they share.