convert/arctrig and convert/arctrigh converts, when possible, the special functions in an expression into arctrigonometric functions, that is, into any of $\arcsin ,\arccos ,\arctan ,\mathrm{arcsec},\mathrm{arccsc},\mathrm{arccot},\mathrm{arcsinh},\mathrm{arccosh},\mathrm{arctanh},\mathrm{arcsech},\mathrm{arccsch},\mathrm{arccoth}$.

$\frac{\frac{1}{2}x{\mathrm{\pi }}^{\frac{1}{2}}}{{\left(-2x^2\right)}^{\frac{1}{4}}}{\left(-2x^2+2\right)}^{\frac{1}{4}}\mathrm{LegendreP}\left(-\frac{1}{2}\,-\frac{1}{2}\,1-2x^2\right)$

$\frac{x\sqrt{\mathrm{\pi }}{\left(-2x^2+2\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}\mathrm{LegendreP}\left(-\frac{1}{2}\,-\frac{1}{2}\,-2x^2+1\right)}{2{\left(-2x^2\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}}$

$\mathrm{convert}\left(\,\mathrm{arctrig}\right)$

$\arcsin \left(x\right)$

$\frac{1}{2}\mathrm{\pi }-\frac{1}{2}x\mathrm{\pi }\mathrm{JacobiP}\left(-\frac{1}{2}\,\frac{1}{2}\,0\,1+2x^2\right)$

$\frac{\mathrm{\pi }}{2}-\frac{x\mathrm{\pi }\mathrm{JacobiP}\left(-\frac{1}{2}\,\frac{1}{2}\,0\,2x^2+1\right)}{2}$

$\mathrm{convert}\left(\,\mathrm{arctrig}\right)$

$\frac{\mathrm{\pi }}{2}-\arctan \left(x\right)$

$\mathrm{JacobiP}\left(-\frac{1}{2}\,\frac{1}{2}\,0\,-\frac{x-3}{x+1}\right)$

$\mathrm{JacobiP}\left(-\frac{1}{2}\,\frac{1}{2}\,0\,-\frac{x-3}{x+1}\right)$

$\mathrm{convert}\left(\,\mathrm{arctrigh}\right)$

$\frac{-2\mathrm{I}\left(x+1\right)\mathrm{arctanh}\left(\frac{\mathrm{I}\sqrt{-\left(x-1\right)\left(x+1\right)}}{x+1}\right)}{\mathrm{\pi }\sqrt{-\left(x-1\right)\left(x+1\right)}}$