New posts in harmonic-numbers

Evaluation of a dilogarithmic integral

sequences-and-series definite-integrals closed-form harmonic-numbers polylogarithm

Existence of a sequence $\{\epsilon_n\}_{n\ge 1}$ such that $\sum\limits_{n=1}^{\infty}\frac{1}{n^{\varepsilon_n}} $ converges

real-analysis sequences-and-series analysis convergence-divergence harmonic-numbers

Finding $\lim\limits_{n\to\infty }\frac{1+\frac12+\frac13+\cdots+\frac1n}{1+\frac13+\frac15+\cdots+\frac1{2n+1}}$

calculus sequences-and-series limits harmonic-numbers

Can one show that $\sum_{n=1}^N\frac{1}{n} -\log N - \gamma \leqslant \frac{1}{2N}$ without using the Euler-Maclaurin formula?

sequences-and-series inequality harmonic-numbers

Prove that $ 1 + \frac{1}{2} + \frac{1}{3} + \cdots + \frac{1}{n} = \mathcal{O}(\log(n)) $.

asymptotics computer-science harmonic-numbers

How to calculate $\int_0^{\frac{\pi}{2}}{x^2\cot x\ln\cos x\, \text{d}x}$.

calculus integration definite-integrals harmonic-numbers digamma-function

Closed form of finite Euler sum $\sum_{k=1}^n \frac{ H_{k}}{(2k+1)}$

summation closed-form harmonic-numbers

Strategies For Summing Harmonic Numbers

calculus sequences-and-series harmonic-numbers

Does there exist a closed form for $L_k$ for any $k>3$?

sequences-and-series closed-form harmonic-numbers

Is the following Harmonic Number Identity true?

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

Two powerful alternating sums $\sum_{n=1}^\infty\frac{(-1)^nH_nH_n^{(2)}}{n^2}$ and $\sum_{n=1}^\infty\frac{(-1)^nH_n^3}{n^2}$

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

What is the closed form of $\sum_{n\geq 1}(-1)^{n-1}\psi'(n)^2$?

sequences-and-series special-functions harmonic-numbers digamma-function

Prove that this subserie of the harmonic series is convergent. [duplicate]

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

Strategies for evaluating sums $\sum_{n=1}^\infty \frac{H_n^{(m)}z^n}{n}$

sequences-and-series definite-integrals closed-form harmonic-numbers polylogarithm

Proving that $\frac{1}{n}+\frac{1}{n+1}+\cdots+\frac{1}{2n}>\frac{13}{24}$ by induction. Where am I going wrong?

inequality summation induction harmonic-numbers

The limit $\lim_{r\to0}\frac1r\left(1-\binom{n}{r}^{-1}\right)$

limits binomial-coefficients gamma-function harmonic-numbers

Connecting noodles probability question

probability harmonic-numbers

Find the limit of the following expression:

limits harmonic-numbers

A series involving inverses of harmonic numbers

sequences-and-series harmonic-numbers

Proof for $\log\frac{2n+1}{n+1}<\frac{1}{n+1}+\frac{1}{n+2}+...+\frac{1}{2n}<\log 2$

real-analysis inequality summation logarithms harmonic-numbers