New posts in polylogarithm

Show that $\sum_{n=0}^{\infty}\frac{2^n(5n^5+5n^4+5n^3+5n^2-9n+9)}{(2n+1)(2n+2)(2n+3){2n\choose n}}=\frac{9\pi^2}{8}$

sequences-and-series pi polylogarithm beta-function

Integral $\int_0^\infty\text{Li}_2\left(e^{-\pi x}\right)\arctan x\,dx$

calculus integration definite-integrals closed-form polylogarithm

Integrals of integer powers of dilogarithm function

integration definite-integrals closed-form riemann-zeta polylogarithm

Conjectural closed-form of $\int_0^1 \frac{\log^n (1-x) \log^{n-1} (1+x)}{1+x} dx$

integration definite-integrals closed-form zeta-functions polylogarithm

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

Yet another log-sin integral $\int\limits_0^{\pi/3}\log(1+\sin x)\log(1-\sin x)\,dx$

integration trigonometry definite-integrals logarithms polylogarithm

Short calculation of the dilogarithm?

special-functions polylogarithm

A closed form for a lot of integrals on the logarithm

real-analysis sequences-and-series definite-integrals closed-form polylogarithm

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

Evaluating $\int_0^1\frac{\operatorname{Li}_2(x)\ln(1+x)}x\,dx$

definite-integrals harmonic-numbers polylogarithm

Integral ${\large\int}_0^1\ln(1-x)\ln(1+x)\ln^2x\,dx$

calculus definite-integrals logarithms harmonic-numbers polylogarithm

A difficult logarithmic integral ${\Large\int}_0^1\log(x)\,\log(2+x)\,\log(1+x)\,\log\left(1+x^{-1}\right)dx$

integration definite-integrals logarithms closed-form polylogarithm

Closed form for ${\large\int}_0^1\frac{\ln(1-x)\,\ln(1+x)\,\ln(1+2x)}{1+2x}dx$

calculus integration definite-integrals logarithms polylogarithm

What is a closed form for ${\large\int}_0^1\frac{\ln^3(1+x)\,\ln^2x}xdx$?

integration logarithms closed-form harmonic-numbers polylogarithm

Triple Euler sum result $\sum_{k\geq 1}\frac{H_k^{(2)}H_k }{k^2}=\zeta(2)\zeta(3)+\zeta(5)$

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

Closed-form of $\int_0^1 \frac{\operatorname{Li}_2\left( x \right)}{\sqrt{1-x^2}} \,dx $

calculus integration definite-integrals closed-form polylogarithm

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

integration definite-integrals special-functions harmonic-numbers polylogarithm

Proof of dilogarithm reflection formula $\zeta(2)-\log(x)\log(1-x)=\operatorname{Li}_2(x)+\operatorname{Li}_2(1-x)$

calculus special-functions polylogarithm

Closed Form for the Imaginary Part of $\text{Li}_3\Big(\frac{1+i}2\Big)$

integration closed-form polylogarithm

Remarkable logarithmic integral $\int_0^1 \frac{\log^2 (1-x) \log^2 x \log^3(1+x)}{x}dx$

integration sequences-and-series closed-form zeta-functions polylogarithm