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Linear relations between logarithmic integrals of high weight and some closed-form evaluations
| Content Provider | Semantic Scholar |
|---|---|
| Author | Au, Kristin C. |
| Copyright Year | 2019 |
| 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. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://arxiv.org/pdf/1910.12113v2.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
