New posts in closed-form

How to find $\int_0^{{\pi}/{2}} (\pi x-4x^2)\log(1+\tan x)\mathrm dx$

integration definite-integrals closed-form

Integral $\int_0^1\frac{x^{42}}{\sqrt{x^4-x^2+1}}\operatorname d \!x$

calculus integration definite-integrals closed-form

A closed form of the double sum $\sum_{m=1}^{\infty}\sum_{n=0}^{m-1}\frac{(-1)^{m-n}}{(m^2-n^2)^2} $

integration sequences-and-series summation closed-form

Calculating $\int_0^\infty \frac{\sin(x)}{x} \frac{\sin(x / 3)}{x / 3} \frac{\sin(x / 5)}{x / 5} \cdots \frac{\sin(x / 15)}{x / 15} \ dx$

integration improper-integrals closed-form products trigonometric-integrals

Improper Integral $\int_0^\infty\left(\frac{\tanh(x)}{x^3}-\frac1{x^2\cosh^2(x)}\right)dx = \frac{7\zeta(3)}{\pi^2} $

calculus integration definite-integrals improper-integrals closed-form

Closed form for ${\large\int}_0^\infty\frac{x-\sin x}{\left(e^x-1\right)x^2}\,dx$

calculus integration definite-integrals improper-integrals closed-form

Harmonic Numbers series I

sequences-and-series generating-functions closed-form catalan-numbers harmonic-numbers

Integral ${\large\int}_0^1\frac{dx}{(1+x^{\sqrt2})^{\sqrt2}}$

integration definite-integrals closed-form gamma-function hypergeometric-function

Is there a closed-form equation for $n!$? If not, why not?

combinatorics algorithms factorial closed-form

Is there a closed form for $\sum_{k=0}^n \frac{x^k}{k!}$? [closed]

summation closed-form

Example equation which does not have a closed-form solution

closed-form elementary-functions

Closed-form of $\int_0^1 \left(\ln \Gamma(x)\right)^3\,dx$

calculus definite-integrals special-functions closed-form gamma-function

Archimedean Clayton copula entropy

probability-theory statistics closed-form entropy copula

Integral $\int_0^1 \frac{\ln(1+x+x^2)\ln(1-x+x^2)}{x}dx$

integration definite-integrals closed-form

An intriguing pattern in Ramanujan's theory of elliptic functions that stops?

integration definite-integrals closed-form hypergeometric-function elliptic-functions

Evaluating $\int_0^{2\pi}\frac{dt}{\sqrt[4]{P(\cos t,\sin t)}}$

calculus integration definite-integrals closed-form

Integral $\int_0^\infty \frac{\arctan(x^2)}{x^4+x^2+1}dx$

integration definite-integrals closed-form

Is there a way to analytically solve $x^\alpha + y^\alpha = \alpha(x + y)$ for $\alpha$, other than $\alpha = 1$?

algebra-precalculus special-functions closed-form

Evaluate $\sum _{n=1}^{\infty } \frac{\sin \left(x \sqrt{a^2+n^2}\right)}{\left(a^2+n^2\right)^{3/2}}$ and generalize it

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

Closed form for $\int_1^\infty\int_0^1\frac{\mathrm dy\,\mathrm dx}{\sqrt{x^2-1}\sqrt{1-y^2}\sqrt{1-y^2+4\,x^2y^2}}$

improper-integrals gamma-function closed-form elliptic-integrals