Some modular relations for the Göllnitz-Gordon functions by an even-odd method
The Göllnitz-Gordon functions are defined as \[ S(q):=\sum_{n=0}^{\infty}\frac{(-q;q^2)_n}{(q^2;q^2)_n}q^{n^2}, \] and \[ T(q):=\sum_{n=0}^{\infty}\frac{(-q;q^2)_n}{(q^2;q^2)_n}q^{n^2+2n}, \] where, as usual, we let \((a;q)_n:=\prod_{j=0}^{n-1}(1-aq^j)\). In this paper the authors provide new proofs of fifteen modular relations for the Göllnitz-Gordon functions, established by \textit{S.-S. Huang} [J. Number Theory 68, No. 2, 178--216 (1998; Zbl 0892.11016)] and \textit{S.-L. Chen} and \textit{S.-S. Huang} [J. Number Theory 93, No. 1, 58--75 (2002; Zbl 1059.11020)], and prove ten new modular relations for these functions using an even-odd method.
scientific article; zbMATH DE number 5971761
scientific article