Integral representations for local dilogarithm and trilogarithm functions
Number Theory
2021-09-28 v2
Abstract
We show new integral representations for dilogarithm and trilogarithm functions on the unit interval. As a consequence, we also prove (1) new integral representations for Apery, Catalan constants, and Legendre chi functions of order 2, 3, (2) a lower bound for the dilogarithm function on the unit interval, (3) new Euler sums.
Keywords
Cite
@article{arxiv.2108.12543,
title = {Integral representations for local dilogarithm and trilogarithm functions},
author = {Masato Kobayashi},
journal= {arXiv preprint arXiv:2108.12543},
year = {2021}
}
Comments
21 pages. This is the second version