New posts in polylogarithm

Log integrals I

integration definite-integrals logarithms polylogarithm

On a property of polylogarithm

calculus complex-analysis polylogarithm

Ways to prove $ \int_0^1 \frac{\ln^2(1+x)}{x}dx = \frac{\zeta(3)}{4}$?

integration sequences-and-series definite-integrals polylogarithm

Double harmonic sum $\sum_{n\geq 1}\frac{H^{(p)}_nH_n}{n^q}$

sequences-and-series polylogarithm

A surprising dilogarithm integral identity arising from a generalised point enclosure problem

geometry definite-integrals geometric-probability polylogarithm

Polylogarithms of negative integer order

stirling-numbers polylogarithm eulerian-numbers

On the integral $\int_{0}^{1/2}\frac{\text{Li}_3(1-z)}{\sqrt{z(1-z)}}\,dz$

integration reference-request special-functions hypergeometric-function polylogarithm

Closed-form of $\int_0^1 \operatorname{Li}_p(x) \, dx$

calculus definite-integrals special-functions closed-form polylogarithm

Evaluating $\int_0^{\pi/2}\operatorname{arcsinh}(2\tan x)\,dx$

calculus integration definite-integrals polylogarithm

Computing $\int_0^1\frac{\ln^3(1-x)\ln(1+x)}{x}dx$ or $\sum_{n=1}^\infty\frac{H_n^{(4)}}{n2^n}$

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

Quadirlogarithm value $\operatorname{Li}_4 \left( \frac{1}{2}\right)$

integration definite-integrals polylogarithm

Yet another difficult logarithmic integral

integration sequences-and-series special-functions hypergeometric-function polylogarithm

Evaluate $\int\limits_0^\infty \frac{\ln^2(1+x)}{1+x^2}\ dx$

real-analysis calculus integration improper-integrals polylogarithm

Evaluate$\int\limits_0^1 [\log(x)\log(1-x)+\operatorname{Li}_2(x)]\left[\frac{\operatorname{Li}_2(x)}{x(1-x)}-\frac{\zeta(2)}{1-x}\right]\mathrm dx$

integration definite-integrals closed-form riemann-zeta polylogarithm

Closed form for $\sum^\infty_{n=1}\frac{H_n}{2^n\,(2n+1)^2}$

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

Conjecture $\int_0^1\frac{\ln^2\left(1+x+x^2\right)}x dx\stackrel?=\frac{2\pi}{9\sqrt3}\psi^{(1)}(\tfrac13)-\frac{4\pi^3}{27\sqrt3}-\frac23\zeta(3)$

definite-integrals logarithms closed-form polylogarithm polygamma

Simplification of a trilogarithm of a complex argument

calculus complex-analysis complex-numbers special-functions polylogarithm

Closed-form of $\int_{0}^{\infty} \frac{{\text{Li}}_2^3(-x)}{x^3}\,dx$

calculus integration definite-integrals closed-form polylogarithm

Closed- form of $\int_0^1 \frac{{\text{Li}}_3^2(-x)}{x^2}\,dx$

calculus integration definite-integrals closed-form polylogarithm

How to evaluate $\int_0^\infty\frac{\frac{\pi^2}{6}-\operatorname{Li}_2\left(e^{-x}\right)-\operatorname{Li}_2\left(e^{-\frac{1}{x}}\right)}{x}dx$

calculus definite-integrals improper-integrals closed-form polylogarithm