The FunctionAdvisor(math_function) command returns the information regarding that function available to the system. The information that displays is organized in sections as shown in the examples.

Although the mathematical information in the sections is all computable (for instance, you can click a formula and explore it by using the operations available in the Context Panel, or just copy and paste it to work with it), it is sometimes convenient to have this information directly presented in a form that is more suitable for further computations. For this purpose use the optional argument table, in which case the same information is presented now as a table where the indices are the topics and the entries are the corresponding information.

The calling sequence FunctionAdvisor(display, math_function) is equivalent to FunctionAdvisor(math_function). Prior to Maple 2016, FunctionAdvisor(math_function) returned a table.

$\mathrm{FunctionAdvisor}\left(\sin \right)$

$\mathrm{sin\_info}≔\mathrm{FunctionAdvisor}\left(\mathrm{table}\,\sin \,\mathrm{quiet}\right)$

$\mathrm{sin\_info}≔table\left(\left[''definition''=\left[\sin \left(z\right)=-\frac{\mathrm{I}}{2}\left({\ⅇ}^{\mathrm{I}z}-\frac{1}{{\ⅇ}^{\mathrm{I}z}}\right)\,\mathrm{with\; no\; restrictions\; on}\left(z\right)\right]\,''classify\_function''=\left(\mathrm{trig}\,\mathrm{elementary}\right)\,''branch\_points''=\left[\sin \left(z\right)\,''No\; branch\; points''\right]\,''symmetries''=\left[\sin \left(-z\right)=-\sin \left(z\right)\,\sin \left(\stackrel{\&conjugate0;}{z}\right)=\stackrel{\&conjugate0;}{\sin \left(z\right)}\right]\,''differentiation\_rule''=\left(\frac{\ⅆ}{\ⅆz}\sin \left(z\right)=\cos \left(z\right)\,\frac{{\ⅆ}^n}{\ⅆz^n}\sin \left(z\right)=\sin \left(z+\frac{n\mathrm{\pi }}{2}\right)\right)\,''describe''=\left(\sin =\mathrm{sine\; function}\right)\,''identities''=\left[\sin \left(\arcsin \left(z\right)\right)=z\,\sin \left(z\right)=-\sin \left(-z\right)\,\sin \left(z\right)=2\sin \left(\frac{z}{2}\right)\cos \left(\frac{z}{2}\right)\,\sin \left(z\right)=\frac{1}{\csc \left(z\right)}\,\sin \left(z\right)=\frac{2\tan \left(\frac{z}{2}\right)}{1+{\tan \left(\frac{z}{2}\right)}^2}\,\sin \left(z\right)=-\frac{\mathrm{I}}{2}\left({\ⅇ}^{\mathrm{I}z}-{\ⅇ}^{\mathrm{-I}z}\right)\,{\sin \left(z\right)}^2=1-{\cos \left(z\right)}^2\,{\sin \left(z\right)}^2=\frac{1}{2}-\frac{\cos \left(2z\right)}{2}\right]\,''sum\_form''=\left[\sin \left(z\right)=\sum _{\mathrm{\_k1}=0}^{\mathrm{\infty }}\frac{{\left(\mathrm{-1}\right)}^{\mathrm{\_k1}}{z}^{2\mathrm{\_k1}+1}}{\left(2\mathrm{\_k1}+1\right)!}\,\mathrm{with\; no\; restrictions\; on}\left(z\right)\right]\,''integral\_form''=\left[\sin \left(z\right)=\frac{z\left({\int }_0^1{\ⅇ}^{2\mathrm{I}\mathrm{\_t1}z}\ⅆ\mathrm{\_t1}\right)}{{\ⅇ}^{\mathrm{I}z}}\,\mathrm{with\; no\; restrictions\; on}\left(z\right)\right]\,''special\_values''=\left[\sin \left(\frac{\mathrm{\pi }}{6}\right)=\frac{1}{2}\,\sin \left(\frac{\mathrm{\pi }}{4}\right)=\frac{\sqrt{2}}{2}\,\sin \left(\frac{\mathrm{\pi }}{3}\right)=\frac{\sqrt{3}}{2}\,\sin \left(\mathrm{\infty }\right)=\mathrm{undefined}\,\sin \left(\mathrm{\infty }\mathrm{I}\right)=\mathrm{\infty }\mathrm{I}\,\left[\sin \left(\mathrm{\pi }n\right)=0\,\wedge \left(n::\mathbb{Z}\right)\right]\,\left[\sin \left(\frac{\left(2n+1\right)\mathrm{\pi }}{2}\right)=\mathrm{-1}\,\wedge \left(n::\mathrm{odd}\right)\right]\,\left[\sin \left(\frac{\left(2n+1\right)\mathrm{\pi }}{2}\right)=1\,\wedge \left(n::\mathrm{even}\right)\right]\right]\,''calling\_sequence''=\sin \left(z\right)\,''periodicity''=\left[\left[\sin \left(2\mathrm{\pi }m+z\right)=\sin \left(z\right)\,\wedge \left(m::\mathbb{Z}\right)\right]\,\left[\sin \left(\mathrm{\pi }m+z\right)={\left(\mathrm{-1}\right)}^m\sin \left(z\right)\,\wedge \left(m::\mathbb{Z}\right)\right]\right]\,''asymptotic\_expansion''=\left(\right)\,''series''=\left(\mathrm{series}\left(\sin \left(z\right)\,z\,4\right)=z-\frac{1}{6}{z}^3+O\left(z^5\right)\right)\,''DE''=\left[f\left(z\right)=\sin \left(z\right)\,\left[\frac{{\ⅆ}^2}{\ⅆz^2}f\left(z\right)=-f\left(z\right)\right]\right]\,''branch\_cuts''=\left[\sin \left(z\right)\,''No\; branch\; cuts''\right]\,''singularities''=\left[\sin \left(z\right)\,z=\mathrm{\infty }+\mathrm{\infty }\mathrm{I}\right]\right]\right)$

$\mathrm{sin\_info}\left[''differentiation\_rule''\right]$

$\frac{\ⅆ}{\ⅆz}\sin \left(z\right)=\cos \left(z\right),\frac{{\ⅆ}^n}{\ⅆz^n}\sin \left(z\right)=\sin \left(z+\frac{n\mathrm{\pi }}{2}\right)$

The FunctionAdvisor/table command was introduced in Maple 2016.

For more information on Maple 2016 changes, see Updates in Maple 2016.