New Modular Relations for the Göllnitz–Gordon Functions Original Research Article

We attempt to obtain new modular relations for the Göllnitz–Gordon functions by techniques which have been used by L. J. Rogers, G. N. Watson, and D. Bressoud to prove some of Ramanujanʹs 40 identities. Also, we give new proofs for some modular relations for the Göllnitz–Gordon functions which have been previously established by using results from L. Rogers and D. Bressoud. Finally, we give applications of those new modular relations to the theory of partitions.