List questions from euler-sums | MathQa

Is there a general method to find $\sum_{i = 1}^{N} i^a$

Published on 13 Jan 2025 - 7:59

On $\int_0^1\frac{\ln(1-e^{\pi i/3}x)}{e^{-\pi i/3}-x}\ln^3xdx$ and its generalization

Published on 12 Jan 2025 - 21:33

An attempt to prove the generalization of $\sum_{n=1}^\infty \frac{(-1)^nH_n}{n^{2a}}$

Published on 12 Jan 2025 - 21:33

Closed form for the skew-harmonic sum $\sum_{n = 1}^\infty \frac{H_n \overline{H}_n}{n^2}$

Published on 12 Jan 2025 - 21:35

Evaluating $\int_0^1 \frac{\ln (1 - x) \operatorname{Li}_2 (-x)}{1 + x} \, dx$

Published on 12 Jan 2025 - 21:26

On the alternating quadratic Euler sum $\sum_{n = 1}^\infty \frac{(-1)^n H_n H_{2n}}{n^2}$

Published on 12 Jan 2025 - 21:34

Binomial Euler sums: Evaluate $\sum_{n=1}^\infty\frac1{4^n}\binom{2n}n\frac{H_n^{(s_1)}\cdots H_n^{(s_k)}}{n^s}$

Published on 12 Jan 2025 - 21:40

Formula for the general case of $\sum_{n=1}^\infty \frac{H_n}{n^2} = 2\zeta(3)$

Published on 12 Jan 2025 - 21:32

Nonlinear alternating Euler sums

Published on 12 Jan 2025 - 21:08

Quadratic Euler Sum $\sum_{n=1}^\infty \frac{(\pm1)^{n-1}}{n^2}\left(\sum_{m=1}^n \frac{(-1)^{m-1}}{2m-1}\right)^2$

Published on 12 Jan 2025 - 21:39