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<p>A new sums-of-tails identity involving two parameters <i>b</i> and <i>d</i> is obtained and is used to derive more results of similar type. One of Ramanujan’s sums-of-tails identities from the Lost Notebook is shown to be a special case of our result. In the course of deriving Ramanujan’s identity, we obtain a new result of combinatorial significance. Two new representations for an infinite series associated to a mock theta function are derived. Also, we give an application of an identity of Andrews and Onofri.</p>

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Some identities of the sums-of-tails type

  • 期刊论文

  • 发表日期：

    2026年2月26日

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  • Atul Dixit,
  • Gaurav Kumar,
  • Aviral Srivastava

摘要

A new sums-of-tails identity involving two parameters b and d is obtained and is used to derive more results of similar type. One of Ramanujan’s sums-of-tails identities from the Lost Notebook is shown to be a special case of our result. In the course of deriving Ramanujan’s identity, we obtain a new result of combinatorial significance. Two new representations for an infinite series associated to a mock theta function are derived. Also, we give an application of an identity of Andrews and Onofri.