arctrig - Maple Help

convert/arctrig

convert logarithms and special functions into arctrigonometric functions

 Calling Sequence convert(expr, arctrig) convert(expr, arctrigh)

Parameters

 expr - Maple expression, equation, or a set or list of them

Description

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

Examples

 > $\frac{\frac{1}{2}x{\mathrm{\pi }}^{\frac{1}{2}}}{{\left(-2{x}^{2}\right)}^{\frac{1}{4}}}{\left(-2{x}^{2}+2\right)}^{\frac{1}{4}}\mathrm{LegendreP}\left(-\frac{1}{2},-\frac{1}{2},1-2{x}^{2}\right)$
 $\frac{{x}{}\sqrt{{\mathrm{\pi }}}{}{\left({-}{2}{}{{x}}^{{2}}{+}{2}\right)}^{{1}}{{4}}}{}{\mathrm{LegendreP}}{}\left({-}\frac{{1}}{{2}}{,}{-}\frac{{1}}{{2}}{,}{-}{2}{}{{x}}^{{2}}{+}{1}\right)}{{2}{}{\left({-}{2}{}{{x}}^{{2}}\right)}^{{1}}{{4}}}}$ (1)
 > $\mathrm{convert}\left(,\mathrm{arctrig}\right)$
 ${\mathrm{arcsin}}{}\left({x}\right)$ (2)
 > $\frac{1}{2}\mathrm{\pi }-\frac{1}{2}x\mathrm{\pi }\mathrm{JacobiP}\left(-\frac{1}{2},\frac{1}{2},0,1+2{x}^{2}\right)$
 $\frac{{\mathrm{\pi }}}{{2}}{-}\frac{{x}{}{\mathrm{\pi }}{}{\mathrm{JacobiP}}{}\left({-}\frac{{1}}{{2}}{,}\frac{{1}}{{2}}{,}{0}{,}{2}{}{{x}}^{{2}}{+}{1}\right)}{{2}}$ (3)
 > $\mathrm{convert}\left(,\mathrm{arctrig}\right)$
 $\frac{{\mathrm{\pi }}}{{2}}{-}{\mathrm{arctan}}{}\left({x}\right)$ (4)
 > $\mathrm{JacobiP}\left(-\frac{1}{2},\frac{1}{2},0,-\frac{x-3}{x+1}\right)$
 ${\mathrm{JacobiP}}{}\left({-}\frac{{1}}{{2}}{,}\frac{{1}}{{2}}{,}{0}{,}{-}\frac{{x}{-}{3}}{{x}{+}{1}}\right)$ (5)
 > $\mathrm{convert}\left(,\mathrm{arctrigh}\right)$
 $\frac{{-}{2}{}{I}{}\left({x}{+}{1}\right){}{\mathrm{arctanh}}{}\left(\frac{{I}{}\sqrt{{-}\left({x}{-}{1}\right){}\left({x}{+}{1}\right)}}{{x}{+}{1}}\right)}{{\mathrm{\pi }}{}\sqrt{{-}\left({x}{-}{1}\right){}\left({x}{+}{1}\right)}}$ (6)