We revisit the umbral methods used by L. J. Rogers in his second proof of the Rogers-Ramanujan identities. we shall study how subsequent methods such as the Bailey chains and their variants arise naturally from Rogers' insights. We conclude with the introduction of multi-dimensional Bailey chains and apply them to prove some new Pentagonal Number Theorems. (C) 2000 Academic Press AMS subject classifications: 11P81, 33D15, 33D80. [References: 13]
展开▼
机译：我们将回顾L. J. Rogers在他对Rogers-Ramanujan身份的第二次证明中使用的本影方法。我们将研究随后的方法（例如Bailey链及其变体）是如何从Rogers的见识中自然产生的。我们以引入多维Bailey链为结尾，并将其应用于证明一些新的五角数定理。 （C）2000 Academic Press AMS主题分类：11P81、33D15、33D80。 [参考：13]
展开▼
