convert/trigh - Maple Help

Home : Support : Online Help : Mathematics : Conversions : Function Class : convert/trigh

convert/trigh

convert exponentials and special functions into hyperbolic functions

 Calling Sequence convert(expr, trigh)

Parameters

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

Description

 • convert/trigh converts the exponentials in an expression as well as the special functions when possible into hyperbolic functions, that is, into any of $\mathrm{sinh},\mathrm{cosh},\mathrm{tanh},\mathrm{sech},\mathrm{csch},\mathrm{coth}$.

Examples

 > ${ⅇ}^{x}$
 ${{ⅇ}}^{{x}}$ (1)
 > $\mathrm{convert}\left(,\mathrm{trigh}\right)$
 ${\mathrm{cosh}}{}\left({x}\right){+}{\mathrm{sinh}}{}\left({x}\right)$ (2)
 > ${\mathrm{π}}^{\frac{1}{2}}\mathrm{MeijerG}\left(\left[\left[\right],\left[\right]\right],\left[\left[\frac{1}{2}\right],\left[0\right]\right],\frac{1{x}^{4}}{4}\right)\mathrm{MeijerG}\left(\left[\left[\right],\left[\right]\right],\left[\left[0\right],\left[\right]\right],-x\right)$
 $\sqrt{{\mathrm{π}}}{}{\mathrm{MeijerG}}{}\left(\left[\left[{}\right]{,}\left[{}\right]\right]{,}\left[\left[\frac{{1}}{{2}}\right]{,}\left[{0}\right]\right]{,}\frac{{1}}{{4}}{}{{x}}^{{4}}\right){}{\mathrm{MeijerG}}{}\left(\left[\left[{}\right]{,}\left[{}\right]\right]{,}\left[\left[{0}\right]{,}\left[{}\right]\right]{,}{-}{x}\right)$ (3)
 > $\mathrm{convert}\left(,\mathrm{trigh}\right)$
 ${-}\frac{\frac{{1}}{{2}}{}{I}{}\sqrt{{4}}{}\sqrt{{{x}}^{{4}}}{}{\mathrm{sinh}}{}\left({I}{}{{x}}^{{2}}\right){}{\mathrm{cosh}}{}\left({x}\right)}{{{x}}^{{2}}}{-}\frac{\frac{{1}}{{2}}{}{I}{}\sqrt{{4}}{}\sqrt{{{x}}^{{4}}}{}{\mathrm{sinh}}{}\left({I}{}{{x}}^{{2}}\right){}{\mathrm{sinh}}{}\left({x}\right)}{{{x}}^{{2}}}$ (4)