Some identities of the sums-of-tails type
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918116068425728 |
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| author | Dixit, Atul Kumar, Gaurav Srivastava, Aviral |
| author_facet | Dixit, Atul Kumar, Gaurav Srivastava, Aviral |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_04365 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some identities of the sums-of-tails type Dixit, Atul Kumar, Gaurav Srivastava, Aviral Combinatorics Number Theory Primary 11P82, Secondary 11P84, 05A17 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. |
| title | Some identities of the sums-of-tails type |
| topic | Combinatorics Number Theory Primary 11P82, Secondary 11P84, 05A17 |
| url | https://arxiv.org/abs/2508.04365 |