A new class of theta-function identities originating in Ramanujan's notebooks
The authors use the theory of modular forms to prove a common generalization of two distinctive theta-function identities stated by Ramanujan. The simpler of Ramanujan's identities is \[ {\textstyle { {{u^ 2} \over v}- {{v^ 2} \over w} + {{w^ 2} \over u}}} =0, \] where \(u= \sum (-1)^ n q^{(7/2) (n-1/ 14)^ 2}\), \(v= \sum (-1)^ n q^{(7/2) (n-3/ 14)^ 2}\), \(w= \sum (-1)^ n q^{(7/2) (n-5/ 14)^ 2}\).
scientific article; zbMATH DE number 645295