The FunctionAdvisor(analytic_extension, math_function) command returns the definition of the analytic extension used by Maple to extend the function outside the classical domain, typically to the entire complex plane.

Note: For most functions the domain of the classical definition is the entire complex plane. If the requested information is not available, the FunctionAdvisor command returns NULL.

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

$\left[\mathrm{\Gamma }\left(z\right)={\int }_0^{\mathrm{\infty }}\frac{{\mathrm{\_k1}}^{z-1}}{{\&ExponentialE;}^{\mathrm{\_k1}}}\&DifferentialD;\mathrm{\_k1}\&comma;0<\mathrm{\Re }\left(z\right)\right]$

$\mathrm{FunctionAdvisor}\left(\mathrm{analytic\_extension}\&comma;\mathrm{\Gamma }\right)$

$\mathrm{\Gamma }\left(z\right)=\frac{\mathrm{\pi }}{\sin \left(\mathrm{\pi }z\right)\mathrm{\Gamma }\left(1-z\right)},\mathrm{\Re }\left(z\right)<0$