New posts in harmonic-numbers

Compute $\int_0^\infty \frac{\operatorname{Li}_3(x)}{1+x^2}\ dx$

integration definite-integrals closed-form harmonic-numbers polylogarithm

Infinite Series $\sum_{n=1}^\infty\frac{H_n}{n^5 2^n}$

real-analysis sequences-and-series closed-form harmonic-numbers zeta-functions

Prove that $\lim_{n\rightarrow \infty} \frac{\log_{10}\lfloor\text{Denominator of } H_{10^n}\rfloor+1 }{10^n}=\log_{10} e$

limits conjectures open-problem harmonic-numbers

Showing $\sum_{k=1}^{nm} \frac{1}{k} \approx \sum_{k=1}^{n} \frac{1}{k} + \sum_{k=1}^{m} \frac{1}{k}$

sequences-and-series harmonic-numbers

Is there a closed form for $\sum_{n=1}^\infty\frac{2^{2n}H_n}{n^3{2n\choose n}}?$

real-analysis integration sequences-and-series binomial-coefficients harmonic-numbers

Identity with Harmonic and Catalan numbers

sequences-and-series generating-functions harmonic-numbers catalan-numbers

A double series $\frac13 \sum_{j=1}^{\infty}\sum_{i=1}^{\infty}\frac{(i-1)! (j-1)!}{(i+j)!}H_{i+j}$ giving $\zeta(3)$

calculus real-analysis sequences-and-series riemann-zeta harmonic-numbers

Assymptotics of the generalized harmonic number $H_{n,r}$ for $r < 1$

summation asymptotics harmonic-numbers

Evaluation of $\sum_{n=0}^{\infty}\frac{1}{(n^4+n^2+1)n!}$

sequences-and-series power-series harmonic-numbers

Interesting Harmonic Sum $\sum_{k\geq 1}\frac{(-1)^{k-1}}{k^2}H_k^{(2)}$

calculus integration sequences-and-series closed-form harmonic-numbers

Integrating $\int_0^1\frac{\ln^2x\ln(1+x)}{1+x^2} dx$ using real methods

real-analysis calculus integration harmonic-numbers polygamma

Another way of expressing $\sum_{k=0}^{n} \frac{H_{k+1}}{n-k+1}$

real-analysis calculus sequences-and-series complex-analysis harmonic-numbers

Harmonic number identity

calculus sequences-and-series binomial-coefficients harmonic-numbers beta-function

Prove $\zeta(3)=2\sum_{n=1}^\infty\frac{H_n}{n}\left[\frac1{4^n}{2n\choose n}\left(H_{2n}-H_n-\frac1{2n}-\ln2\right)+\frac1{2n}\right]$

calculus integration sequences-and-series riemann-zeta harmonic-numbers

Closed form for the harmonic approximation sum $\sum _{k=1}^{\infty } \left(H_k^{(2)}-\zeta (2)\right){}^2$

sequences-and-series approximation harmonic-numbers

Harmonic number inequality

harmonic-numbers

Computing $\int_0^1\frac{\ln^3(1-x)\ln(1+x)}{x}dx$ or $\sum_{n=1}^\infty\frac{H_n^{(4)}}{n2^n}$

integration sequences-and-series closed-form harmonic-numbers polylogarithm

How to evaluate $\int_{0}^{1}\frac{\arctan x}{x} \log{\left(\frac{ 1+ x}{\sqrt{1+x^2}}\right)}\mathrm dx$

calculus integration definite-integrals closed-form harmonic-numbers

Integrating $\int_0^1 \frac{\ln(1+x)\ln^3 x}{1+x}\,dx$ with restricted techniques

calculus integration sequences-and-series definite-integrals harmonic-numbers

Generalized Harmonic Number Summation $ \sum_{n=1}^{\infty} {2^{-n}}{(H_{n}^{(2)})^2}$

real-analysis sequences-and-series generating-functions harmonic-numbers