New posts in euler-sums

A difficult logarithmic integral and its relation to alternating Euler Sums

integration sequences-and-series closed-form harmonic-numbers euler-sums

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

integration sequences-and-series alternative-proof harmonic-numbers euler-sums

Evaluate $\int_0^1 \frac{\ln (1 - x) \ln (1 + x)}{x} \, dx$

integration definite-integrals improper-integrals euler-sums

Calculating alternating Euler sums of odd powers

integration sequences-and-series definite-integrals special-functions euler-sums

Generalized Euler sum $\sum_{n=1}^\infty \frac{H_n}{n^q}$

sequences-and-series riemann-zeta harmonic-numbers euler-sums

Proving an alternating Euler sum: $\sum_{k=1}^{\infty} \frac{(-1)^{k+1} H_k}{k} = \frac{1}{2} \zeta(2) - \frac{1}{2} \log^2 2$

real-analysis calculus sequences-and-series harmonic-numbers euler-sums