关于Schultz对Borweins立方恒等式的推广
On Schultz's generalization of Borweins' cubic identity
AI总结：
本文重新审视Schultz的恒等式，通过两种不同方法推导并给出新证明，同时获得多个新的Schultz型恒等式。
摘要：
1991年，Borweins建立了theta函数的立方类比，被Berndt、Bhargava和Garvan用于研究Ramanujan的椭圆函数立方理论。2013年，Schultz发现了一个三变量theta级数的恒等式，推广了Borweins的恒等式。本文重新审视Schultz的恒等式，提出两种不同的推导方法。我们的研究不仅提供了新的证明，还得到了多个新的Schultz型恒等式。
英文摘要：
In 1991, the Borweins established a cubic analogue of Jacobi's identity for theta functions, which is used by B.C. Berndt, S. Bhargava, and F.G. Garvan in the development of Ramanujan's cubic theory of elliptic functions. In 2013, D. Schultz discovered an identity for theta series in three variables which generalizes the Borweins' identity. In this article, we revisit Schultz's identity and present two distinct approaches to its derivation. Our investigation not only provides new proofs but also yields several new Schultz-type identities.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
