论文标题
一些双币的新证明Rogers-Ramanujan类型身份
New Proofs of Some Double Sum Rogers-Ramanujan Type Identities
论文作者
论文摘要
最近，罗森格伦（Rosengren）使用了一种积分方法来证明Kanade和Russell发现的许多猜想。使用这种积分方法，我们为Rogers-Ramanujan类型的某些双和身份提供了新的证据。这些身份较早地通过诸如组合论证或使用$ q $ -Difference方程的方法证明。我们的证明是基于简化的计算，将这些双和身份与单个总和的一些已知的Rogers-Ramanujan类型身份相关联。此外，我们证明了Andrews和UNCU的猜想身份，该身份早些时候得到了Chern的证实。
Recently, Rosengren utilized an integral method to prove a number of conjectural identities found by Kanade and Russell. Using this integral method, we give new proofs to some double sum identities of Rogers-Ramanujan type. These identities were earlier proved by approaches such as combinatorial arguments or by using $q$-difference equations. Our proofs are based on streamlined calculations, which relate these double sum identities to some known Rogers-Ramanujan type identities with single sums. Moreover, we prove a conjectural identity of Andrews and Uncu which was earlier confirmed by Chern.
