New Computer Algebra Packages for $q$-Series: \texttt{Engel} and \texttt{qMultiSum}

Part one reports on the Mathematica package \texttt{Engel} which was developed jointly with G.E. Andrews (PennState), A. Knopfmacher (Johannesburg), and B. Zimmermann (RISC-Linz). The $q$-Engel Expansion is an algorithm that leads to unique series expansions of $q$-series. Applications concern classical partition theorems, including the Rogers--Ramanujan identities.

Part two is devoted to recent work of A. Riese (RISC-Linz). It concerns a $q$-version of Wegschaider's extension of the Sister Celine/WZ method for the symbolic evaluation of multiple hypergeometric sums. The development of Riese's package \texttt{qMultiSum} is still in an early phase, nevertheless it already produced computer-generated proofs of non-trivial identities, for instance, of key-identities arising in recent work of Alladi, Andrews, and Berkovich.