New posts in harmonic-numbers

Proving $\frac{1}{n+1} + \frac{1}{n+2}+\cdots+\frac{1}{2n} > \frac{13}{24}$ for $n>1,n\in\Bbb N$ by Induction

inequality summation induction harmonic-numbers

Definite Dilogarithm integral $\int^1_0 \frac{\operatorname{Li}_2^2(x)}{x}\, dx $

integration definite-integrals special-functions harmonic-numbers polylogarithm

Conjectured value of a harmonic sum $\sum_{n=1}^\infty\left(H_n-\,2H_{2n}+H_{4n}\right)^2$

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

Infinite Series $\sum\limits_{n=1}^\infty\frac{(H_n)^2}{n^3}$

real-analysis sequences-and-series complex-analysis closed-form harmonic-numbers

Simple proof Euler–Mascheroni $\gamma$ constant

limits logarithms euler-mascheroni-constant harmonic-numbers

Looking for closed-forms of $\int_0^{\pi/4}\ln^2(\sin x)\,dx$ and $\int_0^{\pi/4}\ln^2(\cos x)\,dx$

real-analysis calculus integration improper-integrals harmonic-numbers

Infinite Series $\sum\limits_{n=1}^\infty\left(\frac{H_n}n\right)^2$

real-analysis sequences-and-series complex-analysis closed-form harmonic-numbers

Infinite Series $\sum_{n=1}^\infty\frac{H_n}{n^32^n}$

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

Summing Finitely Many Terms of Harmonic Series: $\sum_{k=a}^{b} \frac{1}{k}$

sequences-and-series harmonic-numbers

Infinite Series $\sum_{n=1}^\infty\frac{H_n}{n^22^n}$

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

Showing that $\lim\limits_{n\to\infty}\sum^n_{k=1}\frac{1}{k}-\ln(n)=0.5772\ldots$ [duplicate]

real-analysis calculus sequences-and-series harmonic-numbers euler-mascheroni-constant

Do harmonic numbers have a “closed-form” expression?

abstract-algebra number-theory functions closed-form harmonic-numbers

Show that $\int_{0}^{\pi/2}\frac {\log^2\sin x\log^2\cos x}{\cos x\sin x}\mathrm{d}x=\frac14\left( 2\zeta (5)-\zeta(2)\zeta (3)\right)$

calculus integration improper-integrals closed-form harmonic-numbers

Alternating harmonic sum $\sum_{k\geq 1}\frac{(-1)^k}{k^3}H_k$

sequences-and-series closed-form harmonic-numbers

Simple proof of showing the Harmonic number $H_n = \Theta (\log n)$

sequences-and-series asymptotics harmonic-numbers

How to find the sum of the series $1+\frac{1}{2}+ \frac{1}{3}+\frac{1}{4}+\dots+\frac{1}{n}$?

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

Proving Binomial Identity without calculus

summation binomial-coefficients harmonic-numbers

A group of important generating functions involving harmonic number.

integration sequences-and-series generating-functions harmonic-numbers polylogarithm

How to find ${\large\int}_0^1\frac{\ln^3(1+x)\ln x}x\mathrm dx$

calculus integration definite-integrals improper-integrals harmonic-numbers

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

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