Chu, Wenchang Generating functions and combinatorial identities. (English) Zbl 0907.05005 Glas. Mat., III. Ser. 33, No. 1, 1-12 (1998). The author establishes an equivalence of the Abel identities and Euler’s binomial theorem, as well as of the Hagen-Rothe identities and Vandermonde’s convolution formula, using the mixed generating function of L. Carlitz for renewal sequences; see L. Carlitz [SIAM J. Math. Anal. 8, No. 3, 518-532 (1977; Zbl 0357.33004)]. As a generalization, he developes two kinds of multifold analogues and their applications to combinatorial identities of multivariate convolutions; see S. G. Mohanty and B. R. Handa [Can. Math. Bull. 12, 45-74 (1969; Zbl 0193.36603)]. Reviewer: I.Strazdins (Riga) Cited in 10 Documents MSC: 05A15 Exact enumeration problems, generating functions 05A19 Combinatorial identities, bijective combinatorics Keywords:Abel identies; Euler’s binomial theorem; Hagen-Rothe identities; generating function; combinatorial identities; multivariate convolutions Citations:Zbl 0357.33004; Zbl 0193.36603 PDFBibTeX XMLCite \textit{W. Chu}, Glas. Mat., III. Ser. 33, No. 1, 1--12 (1998; Zbl 0907.05005)