Linear relations between logarithmic integrals of high weight and some closed-form evaluations

Autor:	Au, K. C.
Rok vydání:	2019
Předmět:	Mathematics - Number Theory
Druh dokumentu:	Working Paper
Popis:	The focus of our investigation will be integrals of form $\int_0^1 \log^a(1-x) \log^b x \log^c(1+x) /f(x) dx$, where $f$ can be either $x,1-x$ or $1+x$. We show that these integrals possess a plethora of linear relations, and give systematic methods of finding them. In lower weight cases, these linear relations yields remarkable closed-forms of individual integrals; in higher weight, we discuss the $\mathbb{Q}$-dimension that such integrals span. Our approach will not feature Euler sums.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1910.12113 Zobrazit plný text záznamu View this record from Arxiv