New posts in Special Functions

Proving that $\int_0^1 \frac{\log^2(x)\tanh^{-1}(x)}{1+x^2}dx=\beta(4)-\frac{\pi^2}{12}G$

Improper Integral $\int_0^1\frac{\arcsin^2(x^2)}{\sqrt{1-x^2}}dx$

How could one solve $\int_{0}^{\infty} \frac{1}{1-t^4}dt$ with special functions?

Conjecture $\sum_{m=1}^\infty\frac{y_{n+1,m}y_{n,k}}{[y_{n+1,m}-y_{n,k}]^3}\overset{?}=\frac{n+1}{8}$, where $y_{n,k}=(\text{BesselJZero[n,k]})^2$

Evaluating a certain integral which generalizes the ${_3F_2}$ hypergeometric function

Is there a function whose antiderivative can be found but whose derivative cannot?

The trigonometric solution to the solvable DeMoivre quintic?

Another beautiful arctan integral $\int_{1/2}^1 \frac{\arctan\left(\frac{1-x^2}{7 x^2+10x+7}\right)}{1-x^2} \, dx$

a conjectured continued fraction for $\tan\left(\frac{z\pi}{4z+2n}\right)$

Prove that $\int_0^\infty\frac{x\cos(x)-\sin(x)}{x\left({e^x}-1\right)}\,dx = \frac{\pi}2+\arg\left(\Gamma(i)\right)-\Re\left(\psi_0(i)\right)$