Chapman, Robin A new proof of some identities of Bressoud. (English) Zbl 1004.05008 Int. J. Math. Math. Sci. 32, No. 10, 627-633 (2002). Summary: We provide a new proof of the following two identities due to Bressoud: \[ \sum_{m=0}^N q^{m^{2}} \left[\begin{matrix} N\\m \end{matrix}\right] = \sum_{m=-\infty}^{\infty} (-1)^m q^{m(5m+1)/2} \left[\begin{matrix} 2N\\N+2m \end{matrix}\right], \]\[ \sum_{m=0}^N q^{m^{2}+m} \left[\begin{matrix} N\\m \end{matrix}\right] = (1/ (1-q^{N+1})) \sum_{m=-\infty}^{\infty} (-1)^m\times q^{m(5m+3)/2} \left[\begin{matrix} 2N+2\\N+2m+2 \end{matrix}\right], \] which can be considered as finite versions of the Rogers-Ramanujan identities. Cited in 3 Documents MSC: 05A19 Combinatorial identities, bijective combinatorics Keywords:Rogers-Ramanujan identities PDFBibTeX XMLCite \textit{R. Chapman}, Int. J. Math. Math. Sci. 32, No. 10, 627--633 (2002; Zbl 1004.05008) Full Text: DOI EuDML