trigh - Maple Help

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

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