Newbetuts

An easier evaluation of $\det\limits_{1\leqslant i,j\leqslant n}\left\{\frac{x_i-x_j}{x_i+x_j}\right\}$

Why is there no general form for the harmonic numbers?

How to prove $\int_{0}^{-1} \frac{\operatorname{Li}_2(x)}{(1-x)^2} dx=\frac{\pi^2}{24}-\frac{\ln^2(2)}{2} $

Conjecture $\int_0^1\frac{\ln\left(\ln^2x+\arccos^2x\right)}{\sqrt{1-x^2}}dx\stackrel?=\pi\,\ln\ln2$

Evaluate $\int_0^1\frac{\ln(1-x)}{x}\text{Li}_3\left(\frac{1+x}{2}\right)dx$ , $\int_0^1\frac{\ln^2(1-x)}{x}\text{Li}_2\left(\frac{1+x}{2} \right)dx$

Closed form for ${\large\int}_0^\infty\frac{x\,\sqrt{e^x-1}}{1-2\cosh x}\,dx$

Evaluting sum $\sum \limits_{n=0}^\infty\frac{n^k}{n!}$

What is the closed form of the $f$ with $f(1)=1$, $f(2)=7$ and $f(n)=7f(n-1)-12f(n-2)$ ($n\ge 3$)?

Are there some techniques which can be used to show that a sum "does not have a closed form"?

Need help with $\int_0^\infty\frac{e^{-x}}{\sqrt[3]2+\cos x}dx$

Proving a formula for $\int_0^\infty \frac{\log(1+x^{4n})}{1+x^2}dx $ if $n=1,2,3,\cdots$

Evaluate $\sum\limits_{n=1}^{\infty}\frac{1}{n^3}\binom{2n}{n}^{-1}$. [duplicate]

Conjectural closed form for $\int_0^\infty\sqrt[3]z\ \operatorname{Ei}^2(-z)\,dz$

On $\int_0^1\arctan\,_6F_5\left(\frac17,\frac27,\frac37,\frac47,\frac57,\frac67;\,\frac26,\frac36,\frac46,\frac56,\frac76;\frac{n}{6^6}\,x\right)\,dx$

New posts in closed-form

An integral $\int^\infty_0\frac{\tanh{x}}{x(1-2\cosh{2x})^2}{\rm d}x$

A couple of definite integrals related to Stieltjes constants

Prove $\sum_{k=1}^\infty\frac{(-1)^{k-1}}{k^32^k {2k\choose k}}=\frac1{4}\zeta(3)-\frac1{6}\ln^32$

Closed form for $\left(-1\right)^{n}\sum_{k=0}^{n}\left(-1\right)^{k}\binom{n}{k}2^{\binom{k}{2}}$

Closed-form of $\int_0^1\left(\frac{\arctan x}{x}\right)^n\,dx$

Evaluate hypergeometric $_6F_5\left(\{\frac12\}_3,\{1\}_3;\{\frac32\}_5;1\right)$

An easier evaluation of $\det\limits_{1\leqslant i,j\leqslant n}\left\{\frac{x_i-x_j}{x_i+x_j}\right\}$

Why is there no general form for the harmonic numbers?

How to prove $\int_{0}^{-1} \frac{\operatorname{Li}_2(x)}{(1-x)^2} dx=\frac{\pi^2}{24}-\frac{\ln^2(2)}{2} $

Conjecture $\int_0^1\frac{\ln\left(\ln^2x+\arccos^2x\right)}{\sqrt{1-x^2}}dx\stackrel?=\pi\,\ln\ln2$

Evaluate $\int_0^1\frac{\ln(1-x)}{x}\text{Li}_3\left(\frac{1+x}{2}\right)dx$ , $\int_0^1\frac{\ln^2(1-x)}{x}\text{Li}_2\left(\frac{1+x}{2} \right)dx$

Closed form for ${\large\int}_0^\infty\frac{x\,\sqrt{e^x-1}}{1-2\cosh x}\,dx$

Evaluting sum $\sum \limits_{n=0}^\infty\frac{n^k}{n!}$

What is the closed form of the $f$ with $f(1)=1$, $f(2)=7$ and $f(n)=7f(n-1)-12f(n-2)$ ($n\ge 3$)?

Are there some techniques which can be used to show that a sum "does not have a closed form"?

Need help with $\int_0^\infty\frac{e^{-x}}{\sqrt[3]2+\cos x}dx$

Proving a formula for $\int_0^\infty \frac{\log(1+x^{4n})}{1+x^2}dx $ if $n=1,2,3,\cdots$

Evaluate $\sum\limits_{n=1}^{\infty}\frac{1}{n^3}\binom{2n}{n}^{-1}$. [duplicate]

Conjectural closed form for $\int_0^\infty\sqrt[3]z\ \operatorname{Ei}^2(-z)\,dz$

On $\int_0^1\arctan\,_6F_5\left(\frac17,\frac27,\frac37,\frac47,\frac57,\frac67;\,\frac26,\frac36,\frac46,\frac56,\frac76;\frac{n}{6^6}\,x\right)\,dx$