International Journal of Mathematics and Mathematical Sciences
Volume 32 (2002), Issue 10, Pages 627-633
doi:10.1155/S0161171202110155
A new proof of some identities of Bressoud
School of Mathematical Sciences, University of Exeter, Exeter EX4 4QE, UK
Received 18 October 2001
Copyright © 2002 Robin Chapman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We provide a new proof of the following two identities due to
Bressoud: ∑m=0Nqm2[Nm]=∑m=−∞∞(−1)mqm(5m+1)/2 [ 2NN+2m], ∑m=0Nqm2+m[Nm]=(1/(1−qN+1))∑m=−∞∞(−1)m×qm(5m+3)/2 [ 2N+2N+2m+2], which can be considered as finite versions of the Rogers-Ramanujan identities.