  Creative telescoping is a powerful computer algebra paradigm -initiated by
Doron Zeilberger in the 90's- for dealing with definite integrals and sums with
parameters. We address the mixed continuous-discrete case, and focus on the
integration of bivariate hypergeometric-hyperexponential terms. We design a new
creative telescoping algorithm operating on this class of inputs, based on a
Hermite-like reduction procedure. The new algorithm has two nice features: it
is efficient and it delivers, for a suitable representation of the input, a
minimal-order telescoper. Its analysis reveals tight bounds on the sizes of the
telescoper it produces.
