A FUNDAMENTAL MODULAR IDENTITY AND SOME APPLICATIONS

We prove a six-parameter identity whose terms have the form x(alpha)T( k1,l1)T(k2, l2) , where T(k, l) = SIGMA(-infinity)infinity x(kn2+ln). This identity is then used to give a new proof of the familiar Ramanuj an identity H(x)G(x11) -x2G(x)H(x11) = 1 , where G(x) = PI(n=0)infinit y[(1 - x5n+1)(1 - x5n+4 )]-1 and H(x) = PI(n=0)infinity[(1 - x5n+2)(1 - X5n+3)]-1. Two other identities, called ''balanced Q2 identities'', are also established through its use.