New posts in closed-form

No closed form for the partial sum of ${n\choose k}$ for $k \le K$?

combinatorics binomial-coefficients closed-form

How can I find $\sum\limits_{n=0}^{\infty}\left(\frac{(-1)^n}{2n+1}\sum\limits_{k=0}^{2n}\frac{1}{2n+4k+3}\right)$?

sequences-and-series closed-form

Integral $\int_0^1 \frac{dx}{\prod_{n=1}^\infty (1+x^n)}$

integration definite-integrals closed-form infinite-product

Definite integral of arcsine over square-root of quadratic

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

Interesting closed form for $\int_0^{\frac{\pi}{2}}\frac{1}{\left(\frac{1}{3}+\sin^2{\theta}\right)^{\frac{1}{3}}}\;d\theta$

calculus definite-integrals closed-form gamma-function elliptic-integrals

Quadruple Integral $\int\limits_0^1\!\!\int\limits_0^1\!\!\int\limits_0^1\!\!\int\limits_0^1\frac1{1-xyzw}\,dw\,dz\,dy\,dx$

real-analysis complex-analysis multivariable-calculus closed-form multiple-integral

Strange closed forms for hypergeometric functions

calculus special-functions gamma-function closed-form hypergeometric-function

Derivative of the Meijer G-function with respect to one of its parameters

calculus complex-analysis derivatives special-functions closed-form

A conjectured value for $\operatorname{Re} \operatorname{Li}_4 (1 + i)$

integration closed-form conjectures polylogarithm

Integral: $\int_0^{\pi} \frac{x}{x^2+\ln^2(2\sin x)}\,dx$

calculus integration definite-integrals closed-form

Integral ${\large\int}_0^1\ln^3\!\left(1+x+x^2\right)dx$

definite-integrals closed-form hypergeometric-function polylogarithm polygamma

Compute close-form of $\int_0^{\frac\pi2}\frac{dt}{\sin t+\cos t+\tan t+\cot t+\csc t+\sec t}$

calculus integration definite-integrals closed-form trigonometric-integrals

Is there a simpler closed form for $\sum_{n=1}^\infty\frac{(2n-1)!!\ (2n+1)!!}{4^n\ (n+2)\ (n+2)!^2}$

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

On Reshetnikov's integral $\int_0^1\frac{dx}{\sqrt[3]x\ \sqrt[6]{1-x}\ \sqrt{1-x\,\alpha^2}}=\frac{1}{N}\,\frac{2\pi}{\sqrt{3}\,|\alpha|}$

calculus integration definite-integrals closed-form experimental-mathematics

How find this series $\sum_{n=1}^{\infty}\frac{1}{n^2H_{n}}$?

sequences-and-series closed-form harmonic-numbers

Closed form for $\int_0^\infty\frac{\sqrt{x+\sqrt{x^2+1}}}{\sqrt{x\phantom{|}}\sqrt{x^2+1}}e^{-x}dx$

calculus integration definite-integrals improper-integrals closed-form

What is the surface area of the 3-dimensional elliptope?

multivariable-calculus definite-integrals analytic-geometry closed-form spectrahedra

A closed form for $\int_0^\infty\left(\frac{2^{-x}-3^{-x}}x\right)^adx,\ a\notin\mathbb{Z}^+$

calculus integration definite-integrals exponential-function closed-form

Simplify $\frac{_3F_2\left(\frac{1}{2},\frac{3}{4},\frac{5}{4};1,\frac{3}{2};\frac{3}{4}\right)}{\Pi\left(\frac{1}{4}\big|\frac{1}{\sqrt{3}}\right)}$

calculus closed-form conjectures hypergeometric-function elliptic-integrals

Prove $\int_0^{\pi/2}{\frac{1+2\cos 2x\cdot\ln\tan x}{1+\tan^{2\sqrt{2}} x}}\tan^{1/\sqrt{2}} x~dx=0$

calculus integration definite-integrals closed-form