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arXiv · 1910.12113

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

K. C. Au
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Abstract

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.

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K. C. Au. 2019-10-26. Linear relations between logarithmic integrals of high weight and some closed-form evaluations. https://arxiv.org/abs/1910.12113

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