New posts in closed-form

are these two continued fractions equivalent?

number-theory closed-form continued-fractions

Is there a name for the closed form of $\sum_{n=0}^{\infty} \frac{1}{1+ a^n}$?

sequences-and-series special-functions closed-form

An interesting integral with log: $\int_{0}^{\pi/2}\ln^2\left(\tan^2\left({x\over 2}\right)\right)\mathrm dx=\frac{\pi^3}2$ [closed]

real-analysis integration definite-integrals closed-form

How to evaluate $\int_0^y\frac{\ln x\ln^2(1-x)}{x}dx$

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

A difficult logarithmic integral and its relation to alternating Euler Sums

integration sequences-and-series closed-form harmonic-numbers euler-sums

Integral $\int_0^1 \frac{\log^4(x)}{(1-x)^4}dx$

integration derivatives proof-verification closed-form polylogarithm

Closed form solution for the (easy at first glance) IVP $wu' =(2-w) u$, $ww'=u-w$

ordinary-differential-equations dynamical-systems closed-form

Ramanujan series Type $\sum _{k=1}^{\infty } \frac{\sinh (2 \pi k)}{2 \sqrt{2} \pi ^9 k^{11} (1-\cosh (2 \pi k))}$

sequences-and-series closed-form

Closed form solution for the zeros of an infinite sum

sequences-and-series roots closed-form

Evaluate $\sum _{n=1}^{\infty } \frac{1}{n^5 2^n \binom{3 n}{n}}$ in terms of elementary constants

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

Conjectured closed form for $\int_0^1\frac{\operatorname{li}^4(x)}{x^4}\,dx$

calculus integration definite-integrals special-functions closed-form

Closed form to an interesting series: $\sum_{n=1}^\infty \frac{1}{1+n^3}$

calculus integration sequences-and-series closed-form digamma-function

Integral $\int_0^1 \frac{\ln(1+x)}{1+x^3}dx$

integration definite-integrals closed-form

Closed-forms of real parts of special value dilogarithm identities from inverse tangent integral function

calculus special-functions closed-form polylogarithm

Integrate $I(a) = \int_0^{\pi/2} \frac{dx}{1-a\sin x}$

calculus integration trigonometry definite-integrals closed-form

Evaluating the limit of a certain definite integral

calculus real-analysis integration limits closed-form

Evaluating $~\int_0^1\sqrt{\frac{1+x^n}{1-x^n}}~dx~$ and $~\int_0^1\sqrt[n]{\frac{1+x^2}{1-x^2}}~dx$

calculus integration definite-integrals closed-form beta-function

Is there a closed form for $\int_a^b\frac{{\rm arccosh}x}{\sqrt{(x-a)(b-x)}}$?

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

Infinite Series $\sum_{m=0}^\infty\sum_{n=0}^\infty\frac{m!\:n!}{(m+n+2)!}$

calculus real-analysis sequences-and-series binomial-coefficients closed-form

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

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