The FunctionAdvisor(definition, math_function) command returns the definition of the function used by the Maple system. This definition is typically in terms of infinite sums or integrals and sometimes in terms of other simpler functions.

$\mathrm{FunctionAdvisor}\left(\mathrm{definition}\,\exp \right)$

$\left[{\ⅇ}^z=\sum _{\mathrm{\_k1}=0}^{\mathrm{\infty }}\frac{z^{\mathrm{\_k1}}}{\mathrm{\_k1}!}\,\mathrm{with\; no\; restrictions\; on}\left(z\right)\right]$

$\mathrm{FunctionAdvisor}\left(\mathrm{definition}\,\mathrm{arccoth}\right)$

$\left[\mathrm{arccoth}\left(z\right)=\frac{\ln \left(z+1\right)}{2}-\frac{\ln \left(z-1\right)}{2}\,\mathrm{with\; no\; restrictions\; on}\left(z\right)\right]$

$\mathrm{FunctionAdvisor}\left(\mathrm{describe}\,\mathrm{arccoth}\right)$

$\mathrm{arccoth}=\mathrm{inverse\; hyperbolic\; cotangent\; function}$

$\mathrm{FunctionAdvisor}\left(\mathrm{definition}\,\mathrm{{\rm B}}\right)$

$\left[\mathrm{{\rm B}}\left(x\,y\right)=\frac{\mathrm{\Gamma }\left(x\right)\mathrm{\Gamma }\left(y\right)}{\mathrm{\Gamma }\left(x+y\right)}\,x::\left(\neg {\mathbb{Z}}^{\left(0\,-\right)}\right)\wedge y::\left(\neg {\mathbb{Z}}^{\left(0\,-\right)}\right)\wedge \left(x+y\right)::\left(\neg {\mathbb{Z}}^{\left(0\,-\right)}\right)\right]$

$\mathrm{depends}\left(\,a\right),\mathrm{depends}\left(\,z\right)$

$\mathrm{false},\mathrm{false}$

$\mathrm{FunctionAdvisor}\left(\mathrm{definition}\,\mathrm{{\rm B}}\left(a\,z\right)\right)$

$\left[\mathrm{{\rm B}}\left(a\,z\right)=\frac{\mathrm{\Gamma }\left(a\right)\mathrm{\Gamma }\left(z\right)}{\mathrm{\Gamma }\left(a+z\right)}\,a::\left(\neg {\mathbb{Z}}^{\left(0\,-\right)}\right)\wedge z::\left(\neg {\mathbb{Z}}^{\left(0\,-\right)}\right)\wedge \left(a+z\right)::\left(\neg {\mathbb{Z}}^{\left(0\,-\right)}\right)\right]$

$\mathrm{depends}\left(\,a\right),\mathrm{depends}\left(\,z\right)$

$\mathrm{true},\mathrm{true}$