New posts in closed-form

Solving for the closed term solution of a third order recurrence relation with real constant coefficients

recurrence-relations closed-form

What is $\mathcal{R}$?

sequences-and-series closed-form gamma-function products spheres

Formula for $\int_0^\infty \frac{\log(1+x^2)}{\sqrt{(a^2+x^2)(b^2+x^2)}}dx$

integration analysis definite-integrals closed-form elliptic-integrals

Closed form for the integral $\int_0^{\pi/2} \frac{x-\sin x}{\tan x-x} dx$

definite-integrals closed-form trigonometric-integrals

Finding $\int^{1}_{0}\frac{\ln^2(x)}{\sqrt{4-x^2}}dx$

real-analysis integration sequences-and-series closed-form

Evaluating by real methods $\int_0^{\pi/2} \frac{x^5}{2-\cos^2(x)}\ dx$

calculus real-analysis integration definite-integrals closed-form

Integral with arithmetic-geometric mean ${\large\int}_0^1\frac{x^z}{\operatorname{agm}(1,\,x)}dx$

calculus integration definite-integrals closed-form elliptic-integrals

Looking for a closed form for a ${}_4 F_3\left(\ldots,1\right)$

sequences-and-series special-functions closed-form hypergeometric-function elliptic-integrals

Rational series representation of $e^\pi$

sequences-and-series exponential-function approximation closed-form pi

Closed form of series with factorial-squared denominator?

sequences-and-series summation factorial closed-form poisson-distribution

Proving $\int_{\sqrt{\frac{3}{5}}}^1 \frac{\arctan (x)}{\sqrt{2 x^2-1} \left(3 x^2-1\right)} \, dx=\frac{3 \pi ^2}{160}$

integration definite-integrals special-functions closed-form

Integral ${\large\int}_0^1\left(-\frac{\operatorname{li} x}x\right)^adx$

definite-integrals logarithms special-functions calculus closed-form

Infinite Series $\sum\limits_{n=1}^\infty\frac{H_{2n+1}}{n^2}$

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

How to compute $\sum_{n\text{ odd}}\frac{1}{n\sinh n\pi\sqrt 3}$?

sequences-and-series closed-form

A conjectured result for $\sum_{n=1}^\infty\frac{(-1)^n\,H_{n/5}}n$

sequences-and-series definite-integrals closed-form harmonic-numbers polylogarithm

Infinite sum of reciprocals of pentagonal numbers

sequences-and-series number-theory convergence-divergence closed-form

Finding a closed form for a recurrence relation $a_n=3a_{n-1}+4a_{n-2}$

linear-algebra recurrence-relations closed-form recursion

On generalizing the harmonic sum $\sum_{n=1}^{\infty}\frac{H_n}{n^k}z^n = S_{k-1,2}(1)+\zeta(k+1)$ when $z=1$?

sequences-and-series definite-integrals closed-form harmonic-numbers polylogarithm

Improper integral : $\int_0^{+\infty}\frac{x\sin x}{x^2+1}$ [closed]

calculus integration definite-integrals improper-integrals closed-form

How to prove $e^x\left|\int_x^{x+1}\sin(e^t) \,\mathrm d t\right|\le 1.4$?

real-analysis optimization closed-form maxima-minima