On an identity by Ercolani, Lega, and Tippings
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911759807283200 |
|---|---|
| author | Yattselev, Maxim L. |
| author_facet | Yattselev, Maxim L. |
| contents | In this note we prove that \[ j!\,2^N \, \binom{N+j-1}{j} \, {}_2F_1\left(\begin{matrix}-j,-2j \\ -N-j+1 \end{matrix};-1\right) = \sum_{l=0}^N \binom{N}{l}\prod_{i=0}^{j-1}2(2i+1+l), \] where $ N $ and $ j $ are positive integers, which resolves a question posed by Ercolani, Lega, and Tippings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09562 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On an identity by Ercolani, Lega, and Tippings Yattselev, Maxim L. Classical Analysis and ODEs 05C30, 33C05 In this note we prove that \[ j!\,2^N \, \binom{N+j-1}{j} \, {}_2F_1\left(\begin{matrix}-j,-2j \\ -N-j+1 \end{matrix};-1\right) = \sum_{l=0}^N \binom{N}{l}\prod_{i=0}^{j-1}2(2i+1+l), \] where $ N $ and $ j $ are positive integers, which resolves a question posed by Ercolani, Lega, and Tippings. |
| title | On an identity by Ercolani, Lega, and Tippings |
| topic | Classical Analysis and ODEs 05C30, 33C05 |
| url | https://arxiv.org/abs/2401.09562 |