Deriving Dilogarithm Identities from the Ratio of Arctangent Integrals
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913088144408576 |
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| author | Hakimoglu-Brown, Cetin |
| author_facet | Hakimoglu-Brown, Cetin |
| contents | Building on results by Abouzahra and Lewin, McIntosh, and Kirilov we derive new functional dilogarithm equations and consequent diologarithim ladders. By showing that the ratio of a pair of sextic and cubic integrals equals a rational constant, we construct new 3- and 6-term functional equations, from which we derive an analytic proof of an identity by Loxton-Lewin, as well as a pair of quartic-base dilogarithm ladders, also believed to be new, building on Loxton's result. Finally, we prove conjectured 2-term dilogarithm identities of Bytsko, and extend his result for the Bloch-Wigner function using the above methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24588 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Deriving Dilogarithm Identities from the Ratio of Arctangent Integrals Hakimoglu-Brown, Cetin Classical Analysis and ODEs 33B30, 33B15 Building on results by Abouzahra and Lewin, McIntosh, and Kirilov we derive new functional dilogarithm equations and consequent diologarithim ladders. By showing that the ratio of a pair of sextic and cubic integrals equals a rational constant, we construct new 3- and 6-term functional equations, from which we derive an analytic proof of an identity by Loxton-Lewin, as well as a pair of quartic-base dilogarithm ladders, also believed to be new, building on Loxton's result. Finally, we prove conjectured 2-term dilogarithm identities of Bytsko, and extend his result for the Bloch-Wigner function using the above methods. |
| title | Deriving Dilogarithm Identities from the Ratio of Arctangent Integrals |
| topic | Classical Analysis and ODEs 33B30, 33B15 |
| url | https://arxiv.org/abs/2604.24588 |