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Results tagged with polylogarithms
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user 512834
For questions about the polylogarithm function, which is a generalization of the natural logarithm.
5
votes
3
answers
818
views
Conjectured closed form of $\int\limits_0^1 \frac{\ln y \operatorname{Li}_2 (-y)}{1-y^2} \, dy$
I uploaded this question here and here from my old account.
Let $\psi^{(1)}$ be the trigamma function defined by
\begin{equation}
\tag{1}
\psi_1(z) = -\int\limits_0^1 \frac{x^{z-1} \ln x}{1-x} \, dx.
…
- 224
1
vote
Conjectured closed form of $\int\limits_0^1 \frac{\ln y \operatorname{Li}_2 (-y)}{1-y^2} \, dy$
Note section:
\begin{align*}
\begin{gathered}
\therefore \sum_{n=0}^{\infty} \frac{(-1)^n H_n^{(2)}}{n^2}=-4 L i_4\left(\frac{1}{2}\right)+\frac{51}{16} \zeta(4)-\frac{7}{2} \ln (2) \zeta(3)+\ln ^2(2) …
- 224