罗杰斯-拉马努扬类等式的一般化

The Ramanujan Journal Pub Date : 2024-08-03 DOI:10.1007/s11139-024-00918-2

Li-Jun Hao, Xueya Kuai, Lan Xia

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摘要

最近，积分法被广泛用于证明一些纳姆问题。在本文中，我们应用这种方法和 \({}_2\phi _1\)数列的三项变换公式建立了一些带参数的多和罗杰斯-拉玛努扬类型的等式。作为特例，我们推导出了已知的罗杰斯-拉马努扬型等式，也发现了一些新的等式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Generalizations of Rogers–Ramanujan type identities

Recently the integral method was widely used to prove some Nahm problems. In the present paper we apply this method and the three-term transformation formula for \({}_2\phi _1\) series to establish some multi-sum Rogers-Ramanujan type identities with parameters. As special cases, we derive known Rogers-Ramanujan type identities, also find some new identities.

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The Ramanujan Journal

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