Alternating Apéry-Type Series and Colored Multiple Zeta Values of Level Eight
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866916880168517632 |
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| author | Xu, Ce Zhao, Jianqiang |
| author_facet | Xu, Ce Zhao, Jianqiang |
| contents | Apéry-type (inverse) binomial series have appeared prominently in the calculations of Feynman integrals in recent years. In our previous work, we showed that a few large classes of the non-alternating Apéry-type (inverse) central binomial series can be evaluated using colored multiple zeta values of level four (i.e., special values of multiple polylogarithms at fourth roots of unity) by expressing them in terms of iterated integrals. In this sequel, we shall prove that for several classes of the alternating versions we need to raise the level to eight. Our main idea is to adopt hyperbolic trigonometric 1-forms to replace the ordinary trigonometric ones used in the non-alternating setting. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2205_01000 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Alternating Apéry-Type Series and Colored Multiple Zeta Values of Level Eight Xu, Ce Zhao, Jianqiang Number Theory 11M32, 11B65, 11B37, 44A05, 11M06, 33B30 Apéry-type (inverse) binomial series have appeared prominently in the calculations of Feynman integrals in recent years. In our previous work, we showed that a few large classes of the non-alternating Apéry-type (inverse) central binomial series can be evaluated using colored multiple zeta values of level four (i.e., special values of multiple polylogarithms at fourth roots of unity) by expressing them in terms of iterated integrals. In this sequel, we shall prove that for several classes of the alternating versions we need to raise the level to eight. Our main idea is to adopt hyperbolic trigonometric 1-forms to replace the ordinary trigonometric ones used in the non-alternating setting. |
| title | Alternating Apéry-Type Series and Colored Multiple Zeta Values of Level Eight |
| topic | Number Theory 11M32, 11B65, 11B37, 44A05, 11M06, 33B30 |
| url | https://arxiv.org/abs/2205.01000 |