Formal sine functions in harmonic algebra
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916796355837952 |
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| author | Kawamura, Hanamichi |
| author_facet | Kawamura, Hanamichi |
| contents | In this paper, we introduce formal sine functions whose coefficients are elements of a generalized harmonic algebra and investigate their properties corresponding to the classical addition formula and Pythagorean theorem. By taking their image under a linear map with some conditions, they coincide with the classical sine function. Moreover, we show that one such linear map is obtained from iterated integrals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_13525 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Formal sine functions in harmonic algebra Kawamura, Hanamichi Number Theory Rings and Algebras 11M32, 33B10 In this paper, we introduce formal sine functions whose coefficients are elements of a generalized harmonic algebra and investigate their properties corresponding to the classical addition formula and Pythagorean theorem. By taking their image under a linear map with some conditions, they coincide with the classical sine function. Moreover, we show that one such linear map is obtained from iterated integrals. |
| title | Formal sine functions in harmonic algebra |
| topic | Number Theory Rings and Algebras 11M32, 33B10 |
| url | https://arxiv.org/abs/2312.13525 |