New posts in closed-form

Prove $_2F_1\left(\frac13,\frac13;\frac56;-27\right)\stackrel{\color{#808080}?}=\frac47$

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

Infinite Series $\sum\limits_{n=1}^{\infty}\frac{1}{\prod\limits_{k=1}^{m}(n+k)}$

real-analysis sequences-and-series closed-form

Closed form for $\int_0^1\frac{x^{5/6}}{(1-x)^{1/6}\,(1+2\,x)^{4/3}}\log\left(\frac{1+2x}{x\,(1-x)}\right)\,dx$

calculus integration definite-integrals logarithms closed-form

Closed form for $\prod_{n=1}^\infty\sqrt[2^n]{\tanh(2^n)},$

calculus closed-form infinite-product hyperbolic-functions trigonometric-series

Closed form of $\mathscr{R}=\int_0^{\pi/2}\sin^2x\,\ln\big(\sin^2(\tan x)\big)\,\,dx$

calculus real-analysis integration closed-form

A closed form of $\sum_{k=1}^\infty \psi^{(1)} (k+a)\psi^{(1)} (k+b)$?

calculus integration sequences-and-series closed-form polygamma

Closed form for integral of integer powers of Sinc function

integration definite-integrals special-functions improper-integrals closed-form

On the general form of the family $\sum_{n=1}^\infty \frac{n^{k}}{e^{2n\pi}-1} $

sequences-and-series closed-form gamma-function bernoulli-numbers

How to evaluate $I=\int\limits_0^{\pi/2}\frac{x\log{\sin{(x)}}}{\sin(x)}\,dx$

integration definite-integrals improper-integrals closed-form

Are there other cases similar to Herglotz's integral $\int_0^1\frac{\ln\left(1+t^{4+\sqrt{15}}\right)}{1+t}\ \mathrm dt$?

calculus integration definite-integrals logarithms closed-form

A closed form for $\int_0^1{_2F_1}\left(-\frac{1}{4},\frac{5}{4};\,1;\,\frac{x}{2}\right)^2dx$

calculus integration special-functions closed-form hypergeometric-function

The entry-level PhD integral: $\int_0^\infty\frac{\sin 3x\sin 4x\sin5x\cos6x}{x\sin^2 x\cosh x}\ dx$

calculus integration trigonometry definite-integrals closed-form

Integral ${\large\int}_0^\infty\frac{\ln x}{1+x}\sqrt{\frac{x+\sqrt{1+x^2}}{1+x^2}}\ \mathrm dx$ [closed]

calculus integration definite-integrals improper-integrals closed-form

What is $\, _4F_3\left(1,1,1,\frac{3}{2};\frac{5}{2},\frac{5}{2},\frac{5}{2};1\right)$?

calculus sequences-and-series closed-form hypergeometric-function

Finding the closed form of a recursive sequence

sequences-and-series closed-form recursion

What's the limit of $\sqrt{2 + \sqrt{2-\sqrt{2+\sqrt{2-\sqrt{2-\sqrt{2 + ...}}}}}} $?

calculus real-analysis limits closed-form nested-radicals

Closed form for the integral $\int_{0}^{\infty}\frac{\ln^{2}(x)\ln(1+x)}{(1-x)(x^{2}+1)}dx$

real-analysis integration definite-integrals improper-integrals closed-form

On the trigonometric roots of a cubic

trigonometry roots closed-form roots-of-unity cubics

Closed form for $\int_0^\infty\arctan\Bigl(\frac{2\pi}{x-\ln\,x+\ln(\frac\pi2)}\Bigr)\frac{dx}{x+1}$ [closed]

calculus integration definite-integrals logarithms closed-form

Integral $\int_0^\infty\frac{\tanh^2(x)}{x^2}dx$

calculus integration definite-integrals closed-form hyperbolic-functions