A new proof of some identities of bressoud

Abstract

We provide a new proof of the following two identities due to Bressoud: ∑ m=0Nq m2 [Nm]=∑ m = -∞∞ (-i)mq m (5m + 1)/2 [ 2NN+2m], ∑ m=0Nq m2+m [Nm]= (1/ (1-q N+1))∑ m = -∞∞ (-1)mxq m (5m+3)/2 [ 2N+2N+2m+2], which can be considered as finite versions of the Rogers-Ramanujan identities. Copyright © 2002 Hindawi Publishing Corporation. All rights reserved.