New posts in harmonic-numbers

Sum $\sum^\infty_{n=1}\frac{(-1)^nH_n}{(2n+1)^2}$

sequences-and-series definite-integrals contour-integration harmonic-numbers polylogarithm

How to approach $\sum _{n=1}^{\infty } \frac{16^n}{n^4 \binom{2 n}{n}^2}$?

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

Prove that ${\sum\limits_{n=1}^{\infty}}(-1)^{n-1} \frac{H_n}{n} = \frac{\pi^2}{12} - \frac12\ln^2 2$

sequences-and-series definite-integrals summation harmonic-numbers

How to compute $\sum_{n=1}^\infty\frac{H_n^2}{n^32^n}$?

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

Evaluate $\sum_{n=1}^\infty\frac{(-1)^{n-1}H_n}{(2n+1)^3}$

real-analysis calculus integration harmonic-numbers polygamma

A generalization of the product of harmonic numbers to non-integer arguments

real-analysis number-theory gamma-function harmonic-numbers oeis

Evaluating $1-\frac12-\frac13+\frac14+\frac15+\frac16-\cdots$

sequences-and-series convergence-divergence closed-form harmonic-numbers

How to evaluate the sum $\sum_{n=1}^{\infty}\frac{1}{(2n+1)(2n+2)}\left(1+\frac{1}{2}+...+\frac{1}{n}\right)$

calculus summation harmonic-numbers

Approximate $\sum\limits_{k=0}^{m-1}\frac{k}{m-k}$

sequences-and-series summation closed-form harmonic-numbers

Tough definite integral: $\int_0^\frac{\pi}{2}x\ln^2(\sin x)~dx$

calculus integration definite-integrals harmonic-numbers

A sum similar to Harmonic numbers.

sequences-and-series limits asymptotics taylor-expansion harmonic-numbers

Another beautiful integral (Part 2)

real-analysis calculus integration definite-integrals harmonic-numbers

Prove that neither $A$ nor $B$ is divisible by $5$

number-theory elementary-number-theory divisibility harmonic-numbers

Integral of polylogarithms and logs in closed form: $\int_0^1 \frac{du}{u}\text{Li}_2(u)^2(\log u)^2$

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

Challenging integral: Evaluate $\int_0^1\frac{\ln^3(1-x)\operatorname{Li}_3(x)}{x}dx$

real-analysis calculus integration definite-integrals harmonic-numbers

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

calculus integration definite-integrals logarithms harmonic-numbers

Test for the convergence of the sequence $S_n =\frac1n \left(1 + \frac{1}{2} + \frac{1}{3} + \cdots+ \frac{1}{n}\right)$

real-analysis sequences-and-series harmonic-numbers

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

integration definite-integrals improper-integrals special-functions harmonic-numbers

Infinite Series $\sum\limits_{n=1}^\infty\frac{H_{2n+1}}{n^2}$

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

Prove that $\int_0^1\frac{\ln(1-x)\ln^2x}{x-1}dx=\frac{\pi^4}{180}$

real-analysis integration definite-integrals improper-integrals harmonic-numbers