Evaluation of one-dimensional polylogarithmic integral, with applications to infinite series
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866914654742118400 |
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| author | Au, Kam Cheong |
| author_facet | Au, Kam Cheong |
| contents | We give systematic method to evaluate a large class of one-dimensional integral relating to multiple zeta values (MZV) and colored MZV. We also apply the technique of iterated integrals and regularization to elucidate the nature of some infinite series involving binomial coefficients. This technique can be applied to many Apéry-type infinite sums. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_03957 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Evaluation of one-dimensional polylogarithmic integral, with applications to infinite series Au, Kam Cheong Number Theory Classical Analysis and ODEs 11M32 (Primary), 33C20 (Secondary) We give systematic method to evaluate a large class of one-dimensional integral relating to multiple zeta values (MZV) and colored MZV. We also apply the technique of iterated integrals and regularization to elucidate the nature of some infinite series involving binomial coefficients. This technique can be applied to many Apéry-type infinite sums. |
| title | Evaluation of one-dimensional polylogarithmic integral, with applications to infinite series |
| topic | Number Theory Classical Analysis and ODEs 11M32 (Primary), 33C20 (Secondary) |
| url | https://arxiv.org/abs/2007.03957 |