New posts in harmonic-numbers

A Gift Problem for the Year 2018 [duplicate]

combinatorics group-theory summation finite-groups harmonic-numbers

$-4\zeta(2)-2\zeta(3)+4\zeta(2)\zeta(3)+2\zeta(5)=S$

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

Prove that $\int_0^1\frac{x\ln (1+x)}{1+x^2}dx=\frac{\pi^2}{96}+\frac{\ln^2 2}{8}$

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

Which harmonic numbers have prime numerators?

number-theory fractions harmonic-numbers

How find this series $\sum_{n=1}^{\infty}\frac{1}{n^2H_{n}}$?

sequences-and-series closed-form harmonic-numbers

Proving that $~\sum\limits_{k=2}^{\infty}\frac{(-1)^k}{k^2}~H_k~H_{k-1}=\frac{3}{16}~\zeta(4)$

calculus sequences-and-series definite-integrals contest-math harmonic-numbers

How find this $\sum_{n=1}^{\infty}\frac{H^3_{n}}{n+1}(-1)^{n+1}$

sequences-and-series summation harmonic-numbers

Is there any formula for the series $1 + \frac12 + \frac13 + \cdots + \frac 1 n = ?$

sequences-and-series algebra-precalculus summation harmonic-numbers

A series involves harmonic number

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

Is this a valid proof that the harmonic series diverges?

sequences-and-series solution-verification harmonic-numbers

nice two related sums $\sum_{n=1}^\infty\frac{(-1)^nH_n^{(2)}}{n^2}$ and $\sum_{n=1}^\infty\frac{(-1)^nH_n^2}{n^2}$

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

Integral $\int_0^1\frac{\log(x)\log^2(1-x)\log^2(1+x)}{x}\mathrm dx$

calculus integration improper-integrals closed-form harmonic-numbers

A "binomial" generalization of harmonic numbers

binomial-coefficients integer-partitions harmonic-numbers

Prove that $\int_0^1 \frac{{\rm{Li}}_2(x)\ln(1-x)\ln^2(x)}{x} \,dx=-\frac{\zeta(6)}{3}$

real-analysis integration definite-integrals harmonic-numbers polylogarithm

prove $\ln(1+x^2)\arctan x=-2\sum_{n=1}^\infty \frac{(-1)^n H_{2n}}{2n+1}x^{2n+1}$

real-analysis calculus generating-functions closed-form harmonic-numbers

How to calculate $\sum_{n=1}^\infty\frac{(-1)^n}n H_n^2$?

calculus sequences-and-series recurrence-relations closed-form harmonic-numbers

What would Gauss do in this case: adding $1+\frac12+\frac13+\frac14+ \dots +\frac1{100}$?

elementary-number-theory arithmetic harmonic-numbers

Compute $\int_0^{\pi/2} x^2\left(\sum_{n=1}^\infty (-1)^{n-1} \cos^n(x)\cos(nx)\right)dx$

calculus integration sequences-and-series harmonic-numbers polylogarithm

Evaluation of $\int_0^1 \frac{\log^2(1+x)}{x} \ dx$

real-analysis calculus integration definite-integrals harmonic-numbers

On binomial sums $\sum_{n=1}^\infty \frac{1}{n^k\,\binom {2n}n}$ and log sine integrals

riemann-zeta harmonic-numbers experimental-mathematics definite-integrals binomial-coefficients