New posts in closed-form

Sum of the series $\sum\limits_{n=0}^\infty \frac{1}{(3n+1)^3}$

sequences-and-series closed-form

Approximate $\sum\limits_{k=0}^{m-1}\frac{k}{m-k}$

sequences-and-series summation closed-form harmonic-numbers

How to evaluate improper integral $\int_{0}^{\infty}\frac{\tan^{-1}{x}}{e^{ax}-1}dx$?

integration definite-integrals improper-integrals closed-form

closed form of $\sum \frac{1}{z^3 - n^3}$

sequences-and-series complex-analysis closed-form

Evaluating $\int{ \frac{x^n}{1 + x + \frac{x^2}{2} + \cdots + \frac{x^n}{n!}}}dx$ using Pascal inversion

calculus real-analysis integration indefinite-integrals closed-form

Does there exist a closed form for the sinc function series $\sum_{n=1}^\infty \frac{\sin\sqrt{n^2+1}}{\sqrt{n^2+1}}$?

sequences-and-series closed-form

What would qualify as a valid reason to believe there is a closed form?

integration soft-question special-functions closed-form philosophy

Closed form for $\int_0^e\mathrm{Li}_2(\ln{x})\,dx$?

integration definite-integrals special-functions closed-form polylogarithm

$\int_0^\infty(\log x)^2(\mathrm{sech}\,x)^2\mathrm dx$

improper-integrals closed-form hyperbolic-functions

Integral of polylogarithms and logs in closed form: $\int_0^1 \frac{du}{u}\text{Li}_2(u)^2(\log u)^2$

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

Integral ${\large\int}_0^1\frac{\ln^2\ln\left(\frac1x\right)}{1+x+x^2}dx$

calculus integration definite-integrals logarithms closed-form

Closed form for $\sum_{n=1}^\infty\frac{(-1)^n n^a H_n}{2^n}$

sequences-and-series summation gamma-function closed-form

Does $\int_0^{\infty} \left( p + q W \left( r e^{- s x + t} \right) + u x \right) e^{- x} d x$ have a closed-form expression?

integration closed-form lambert-w

Closed form for $\sum_{n=1}^\infty\frac{\cos(\pi \log n)}{n^2}$

sequences-and-series logarithms closed-form trigonometric-series

How to integrate $\int_{0}^{\infty }{\frac{\sin x}{\cosh x+\cos x}\cdot \frac{{{x}^{n}}}{n!}\ \text{d}x} $?

calculus integration definite-integrals improper-integrals closed-form

Closed form for n-th anti-derivative of $\log x$

calculus integration logarithms closed-form

Formula for $\sum_{k=1}^n \frac{1}{k(k+1)(k+2)}$?

sequences-and-series summation closed-form

Evaluate $\int_0^1\int_0^1 \left\{ \frac{e^x}{e^y} \right\}dxdy$

integration multivariable-calculus proof-verification closed-form fractional-part

Closed form of $I=\int_{0}^{\pi/2} \tan^{-1} \bigg( \frac{\cos(x)}{\sin(x) - 1 - \sqrt{2}} \bigg) \tan(x)\;dx$

calculus integration definite-integrals contour-integration closed-form

Help with logarithmic definite integral: $\int_0^1\frac{1}{x}\ln{(x)}\ln^3{(1-x)}\, dx$

integration definite-integrals logarithms improper-integrals closed-form