Chapman, Robin Franklin’s argument proves an identity of Zagier. (English) Zbl 0962.05011 Electron. J. Comb. 7, No. 1, Research paper R54, 5 p. (2000); printed version J. Comb. 7, No. 2 (2000). The following remarkable identity of D. Zagier (to appear in Topology) \[ \sum^\infty_{n= 0} [(q)_\infty- (q)_n]= (q)_\infty \sum^\infty_{k= 1}{q^k\over 1- q^k}+ \sum^\infty_{r= 1}(-1)^r [(3r- 1) q^{r(3r- 1)/2}+ 3rq^{r(3r+ 1)/2}] \] is proved by a slight modification of Franklin’s well-known involution proof of Euler’s pentagonal number theorem. Reviewer: László A.Székely (Columbia/South Carolina) Cited in 4 Documents MSC: 05A17 Combinatorial aspects of partitions of integers 11P81 Elementary theory of partitions Keywords:partitions of integers; Franklin’s involution PDFBibTeX XMLCite \textit{R. Chapman}, Electron. J. Comb. 7, No. 1, Research paper R54, 5 p. (2000; Zbl 0962.05011) Full Text: arXiv EuDML EMIS Online Encyclopedia of Integer Sequences: Coefficients of q in series expansion of Zagier’s identity.