On Euler's formulae for double zeta values
Number Theory
2016-10-27 v2
Abstract
In 1776, L. Euler proposed three methods, called prima methodus, secunda methodus and tertia methodus, to calculate formulae for double zeta values. However strictly speaking, his last two methods are mathematically incomplete and require more precise reformulation and more sophisticated arguments for their justification. In this paper, we reformulate his formulae, give their rigorous proofs and also clarify that the formulae can be derived from the extended double shuffle relations.
Keywords
Cite
@article{arxiv.1604.04463,
title = {On Euler's formulae for double zeta values},
author = {Ryotaro Harada},
journal= {arXiv preprint arXiv:1604.04463},
year = {2016}
}
Comments
8 pages. To appear in Kyushu J.M