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<p>The Rogers–Ramanujan identities were first proved by Rogers in 1894 and later rediscovered by Ramanujan around 1913. During the study of these two identities, many Rogers–Ramanujan type identities have been found, and these identities have always been of great interest to mathematicians. In this paper, by means of properties of Appell–Lerch sums in combination with Bailey pairs and Bailey’s lemma, we derive some generalizations of Rogers–Ramanujan type identities, which include some known identities and also imply some new ones.</p>

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Generalizations of Rogers–Ramanujan type identities

  • 期刊论文

  • 发表日期：

    2025年8月4日

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  • Su-Ping Cui,
  • Nancy S. S. Gu,
  • Qian Wang

摘要

The Rogers–Ramanujan identities were first proved by Rogers in 1894 and later rediscovered by Ramanujan around 1913. During the study of these two identities, many Rogers–Ramanujan type identities have been found, and these identities have always been of great interest to mathematicians. In this paper, by means of properties of Appell–Lerch sums in combination with Bailey pairs and Bailey’s lemma, we derive some generalizations of Rogers–Ramanujan type identities, which include some known identities and also imply some new ones.