Two closed-form evaluations for the generalized hypergeometric function ${}_4F_3(\frac1{16})$
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866909454634582016 |
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| author | Rathie, Arjun K. Shpot, Mykola A. |
| author_facet | Rathie, Arjun K. Shpot, Mykola A. |
| contents | The objective of this short note is to provide two closed-form evaluations for the generalized hypergeometric function $_4F_3$ of the argument $\frac1{16}$. This is achieved by means of separating a generalized hypergeometric function $_3F_2$ into even and odd components, together with the use of two known results for $_3F_2(\pm\frac14)$ available in the literature. As an application, we obtain an interesting infinite-sum representation for the number $π^2$. Certain connections with the work of Ramanujan and other authors are discussed, involving other special functions and binomial sums of different kinds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_07664 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Two closed-form evaluations for the generalized hypergeometric function ${}_4F_3(\frac1{16})$ Rathie, Arjun K. Shpot, Mykola A. Classical Analysis and ODEs 33C20, 33C05, 33C15 The objective of this short note is to provide two closed-form evaluations for the generalized hypergeometric function $_4F_3$ of the argument $\frac1{16}$. This is achieved by means of separating a generalized hypergeometric function $_3F_2$ into even and odd components, together with the use of two known results for $_3F_2(\pm\frac14)$ available in the literature. As an application, we obtain an interesting infinite-sum representation for the number $π^2$. Certain connections with the work of Ramanujan and other authors are discussed, involving other special functions and binomial sums of different kinds. |
| title | Two closed-form evaluations for the generalized hypergeometric function ${}_4F_3(\frac1{16})$ |
| topic | Classical Analysis and ODEs 33C20, 33C05, 33C15 |
| url | https://arxiv.org/abs/2303.07664 |