In this paper, we revisit an identity which was proven by Ramanujan and from which he deduced the famous identities that are named after him and L. J. Rogers. Unlike Ramanujan’s proof (which uses the method of q-difference equations), we examine directly the q-coefficients involved. We isolate and identify terms that cancel each other. Once these terms are paired up and canceled, we only need the geometric series to complete the proof.

中文翻译：

---

追逐取消：重新审视暗示罗杰斯-拉马努金身份的经典身份

在本文中，我们重新审视了 Ramanujan 证明的身份，并从中推断出以他和 LJ Rogers 命名的著名身份。与 Ramanujan 的证明不同（它使用q-差分方程），我们直接检查q- 涉及的系数。我们隔离并识别相互抵消的术语。一旦这些项配对并取消，我们只需要几何级数即可完成证明。