convert/arctrig - Maple Programming Help

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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

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

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