New posts in harmonic-numbers

Positivity of a certain sum of Stirling numbers

combinatorics harmonic-numbers stirling-numbers eulerian-numbers

Prove $\sum_{n=0}^\infty(-1)^n(\overline{H}_n-\ln2)^2=\frac{\pi^2}{24}$

calculus integration sequences-and-series alternative-proof harmonic-numbers

How to evaluate $\int_0^y\frac{\ln x\ln^2(1-x)}{x}dx$

integration sequences-and-series generating-functions closed-form harmonic-numbers

Is there a closed form for the alternating series of inverse harmonic numbers?

sequences-and-series harmonic-numbers

A difficult logarithmic integral and its relation to alternating Euler Sums

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

Expanding integers into distinct egyptian fractions - what is the optimal way?

elementary-number-theory fractions harmonic-numbers egyptian-fractions

Prove $\sum_{n=0}^\infty(-1)^n(\overline{H}_n-\ln2)^3=-\frac5{16}\zeta(3)$

calculus integration sequences-and-series alternative-proof harmonic-numbers

Evaluating $\int _0^1\frac{\ln ^2\left(x\right)\ln \left(1-x\right)}{1+x^2}\:dx$

integration definite-integrals improper-integrals harmonic-numbers

How to compute $\int_0^1\frac{\text{Li}_2(x^2)\arcsin^2(x)}{x}dx$ or $\sum_{n=1}^\infty\frac{4^nH_n}{n^4{2n\choose n}}$

real-analysis integration trigonometry harmonic-numbers polylogarithm

Evaluate $\sum _{n=1}^{\infty } \frac{1}{n^5 2^n \binom{3 n}{n}}$ in terms of elementary constants

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

Contest math problem: $\sum_{n=1}^\infty \frac{\{H_n\}}{n^2}$

summation contest-math harmonic-numbers

Get a good approximation of $\int_0^1 \left(H_x\right)^2 dx$, where $H_x$ is the generalized harmonic number

real-analysis integration definite-integrals numerical-methods harmonic-numbers

Is there a closed a form for $\sum_{n=1}^\infty\frac{(-1)^{n-1}H_{an}}{n}\,?$

real-analysis integration complex-analysis closed-form harmonic-numbers

How to evaluate $ \sum\limits_{n=1}^{\infty} \left( \frac{H_{n}}{(n+1)^2.2^n} \right)$

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

Evaluate $\int_0^1\frac{\ln x\ln(1-x)}{1+x^2}\ dx$

calculus integration definite-integrals harmonic-numbers polylogarithm

An Euler type sum: $\sum_{n=1}^{\infty}\frac{H_n^{(2)}}{n\cdot 4^n}{2n \choose n}$, where $H_n^{(2)}=\sum\limits_{k=1}^{n}\frac{1}{k^2}$

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

Computing $\sum_{n=1}^\infty\frac{2^{2n}H_{n+1}}{(n+1)^2{2n\choose n}}$

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

Infinite series with harmonic numbers related to elliptic integrals

sequences-and-series special-functions generating-functions harmonic-numbers elliptic-integrals

Evaluate $\int_0^1\frac{\ln(1-x)\ln(1+x)}{1+x^2}dx$

calculus integration definite-integrals closed-form harmonic-numbers

Closed form expression for the harmonic sum $\sum\limits_{n=1}^{\infty}\frac{H_{2n}}{n^2\cdot4^n}{2n \choose n}$

real-analysis sequences-and-series definite-integrals binomial-coefficients harmonic-numbers