Formal sine functions in harmonic algebra
Number Theory
2025-06-18 v2 Rings and Algebras
Abstract
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.
Cite
@article{arxiv.2312.13525,
title = {Formal sine functions in harmonic algebra},
author = {Hanamichi Kawamura},
journal= {arXiv preprint arXiv:2312.13525},
year = {2025}
}