New posts in closed-form

What is the antiderivative of $e^{-x^2}$

calculus integration indefinite-integrals closed-form error-function

Evaluating $\int_0^\infty \frac{dx}{\sqrt{x}[x^2+(1+2\sqrt{2})x+1][1-x+x^2-x^3+...+x^{50}]}$

calculus integration definite-integrals improper-integrals closed-form

Closed form for $\sum_{n=-\infty}^{\infty}\frac{1}{(n-a)^2+b^2}$.

calculus sequences-and-series complex-analysis fourier-analysis closed-form

Prove that $\int_{0}^{1}\sin{(\pi x)}x^x(1-x)^{1-x}\,dx =\frac{\pi e}{24} $

calculus integration definite-integrals closed-form

Is it possible to simplify $\frac{\Gamma\left(\frac{1}{10}\right)}{\Gamma\left(\frac{2}{15}\right)\ \Gamma\left(\frac{7}{15}\right)}$?

calculus special-functions closed-form gamma-function

Infinite Series $\sum\limits_{n=1}^\infty\left(\frac{H_n}n\right)^2$

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

Finite Sum $\sum\limits_{k=1}^{m-1}\frac{1}{\sin^2\frac{k\pi}{m}}$

analysis trigonometry summation closed-form fractions

Evaluating the infinite product $\prod\limits_{k=2}^\infty \left ( 1-\frac1{k^2}\right)$

sequences-and-series limits closed-form products infinite-product

Closed Form for $~\int_0^1\frac{\text{arctanh }x}{\tan\left(\frac\pi2~x\right)}~dx$

calculus integration definite-integrals improper-integrals closed-form

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

integration closed-form polylogarithm

How is Faulhaber's formula derived?

summation exponentiation closed-form

Infinite Series $\sum_{n=1}^\infty\frac{H_n}{n^32^n}$

real-analysis sequences-and-series closed-form harmonic-numbers zeta-functions

Infinite Series $‎\sum\limits_{n=2}^{\infty}\frac{\zeta(n)}{k^n}$

real-analysis sequences-and-series complex-analysis closed-form riemann-zeta

Integral $\int_0^1\frac{\ln\left(x+\sqrt2\right)}{\sqrt{2-x}\,\sqrt{1-x}\,\sqrt{\vphantom{1}x}}\mathrm dx$

calculus integration definite-integrals logarithms closed-form

Closed form for $\int_0^1\log\log\left(\frac{1}{x}+\sqrt{\frac{1}{x^2}-1}\right)\mathrm dx$

calculus integration logarithms definite-integrals closed-form

Infinite Series $\sum_{n=1}^\infty\frac{H_n}{n^22^n}$

real-analysis sequences-and-series closed-form zeta-functions harmonic-numbers

Conjecture $_2F_1\left(\frac14,\frac34;\,\frac23;\,\frac13\right)=\frac1{\sqrt{\sqrt{\frac4{\sqrt{2-\sqrt[3]4}}+\sqrt[3]{4}+4}-\sqrt{2-\sqrt[3]4}-2}}$

calculus special-functions closed-form conjectures hypergeometric-function

Integral $\int_1^\infty\frac{\operatorname{arccot}\left(1+\frac{2\pi}{\operatorname{arcoth}x-\operatorname{arccsc}x}\right)}{\sqrt{x^2-1}}\mathrm dx$

integration trigonometry closed-form conjectures hyperbolic-functions

What does closed form solution usually mean?

soft-question closed-form

Closed form for $\int_0^\infty\ln\frac{J_\mu(x)^2+Y_\mu(x)^2}{J_\nu(x)^2+Y_\nu(x)^2}\mathrm dx$

special-functions improper-integrals closed-form