An algorithmic approach to discovering and proving \(q\)-series identities
The present paper deals with an algorithmic method for proving \(q\)-series identities based on the extended Engel Expansion Theorem, i.e., the general inverse polynomial expansion method for Laurent series [\textit{A. Knopfmacher} and \textit{J. Knopfmacher}, Constructive Approximation 4, No. 4, 379-389 (1988; Zbl 0659.41024)] and constitutes a complement to the algorithms by Gosper, Wilf and Zeilberger, among others [see e.g. the nice book of \textit{M. Petkovsek, H. S. Wilf} and \textit{D. Zeilberger}, \(A=B\). With foreword by Donald E. Knuth (1996; Zbl 0848.05002)]. As illustrating examples the authors show a new proof of the Gauss identity \[ \sum_{n=0}^{\infty}q^{n(n+1)/2}=\frac{(q^2,q^2)_\infty} {(q,q^2)_\infty}, \] as well as two Rogers-Ramanujan identities.
scientific article; zbMATH DE number 1563059