New posts in closed-form

A conjectured identity for tetralogarithms $\operatorname{Li}_4$

logarithms special-functions closed-form conjectures polylogarithm

Closed form for integral $\int_{0}^{\pi} \left[1 - r \cos\left(\phi\right)\right]^{-n} \phi \,{\rm d}\phi$

calculus integration definite-integrals closed-form

Why is this definite integral antisymmetric in $s\mapsto s^{-1}$?

calculus definite-integrals closed-form symmetry

Integral $\int_0^\frac{\pi}{2} x^2\sqrt{\tan x}\,\mathrm dx$

integration definite-integrals closed-form alternative-proof

Evaluate $\int_{0}^1 \prod_{k=2}^n \lfloor kx \rfloor dx$

calculus elementary-number-theory definite-integrals closed-form

Improper Integral $\int\limits_0^{\frac12}(2x - 1)^6\log^2(2\sin\pi x)\,dx$

calculus real-analysis integration improper-integrals closed-form

Extract real and imaginary parts of $\operatorname{Li}_2\left(i\left(2\pm\sqrt3\right)\right)$

calculus complex-analysis special-functions closed-form polylogarithm

Peculiar Sum regarding the Reciprocal Binomial Coefficients

sequences-and-series definite-integrals summation binomial-coefficients closed-form

Evaluating $\sum_{n \geq 1}\ln \!\left(1+\frac1{2n}\right) \!\ln\!\left(1+\frac1{2n+1}\right)$

calculus integration sequences-and-series logarithms closed-form

Closed form for $\int_0^1 \frac {\log^n(x)}{(1-x)^m} dx$

integration closed-form

Compute $\int_0^{1/2}\frac{\left(\operatorname{Li}_2(x)\right)^2}{x}dx$ or $\sum_{n=1}^\infty \frac{H_n^{(2)}}{n^32^n}$

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

Solving the integral $\int_0^{\pi/2}\log\left(\frac{2+\sin2x}{2-\sin2x}\right)\mathrm dx$

integration definite-integrals closed-form

Proving that $\int_0^\infty\Big(\sqrt[n]{1+x^n}-x\Big)dx~=~\frac12\cdot{-1/n\choose+1/n}^{-1}$

calculus integration definite-integrals closed-form beta-function

Generalizing two infinite products for $\operatorname{sinc}(x)$ and their 'dual' infinite product

trigonometry convergence-divergence special-functions closed-form infinite-product

Inverse Trigonometric Integrals

calculus integration definite-integrals improper-integrals closed-form

Closed form for an infinite product

closed-form infinite-product

Closed form of $\int_0^\pi \frac{\sin(x)}{\sqrt{x^3+x+1}} dx$

integration definite-integrals closed-form

Determining the number of valid TicTacToe board states in terms of board dimension

combinatorics graph-theory game-theory closed-form combinatorial-game-theory

Evaluation of $\sum_{x=0}^\infty e^{-x^2}$

sequences-and-series integration special-functions closed-form

Need help with $\int_0^\infty x^{-\frac{3}{2}}\ \text{Li}_{\sqrt{2}}(-x)\ dx$

special-functions improper-integrals closed-form