display - Maple Help

display information about a mathematical function organized in sections

return a table of information about a mathematical function

Parameters

 math_function - name of known mathematical function; see type/mathfunc display - (optional) literal name 'display' table - (optional) literal name 'table'; return a table of information about math_function

Description

 • 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.

Examples

The information about a mathematical function organized in closed sections

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

sin

describe

 ${\mathrm{sin}}{=}{\mathrm{sine function}}$

definition

 ${\mathrm{sin}}\left({z}\right){=}{-}\frac{{I}}{{2}}{}\left({{ⅇ}}^{{I}{}{z}}{-}\frac{{1}}{{{ⅇ}}^{{I}{}{z}}}\right)$ ${\mathrm{with no restrictions on}}\left({z}\right)$

classify function

 ${\mathrm{trig}}$ ${\mathrm{elementary}}$

symmetries

 ${\mathrm{sin}}\left({-}{z}\right){=}{-}{\mathrm{sin}}\left({z}\right)$ ${\mathrm{sin}}\left(\stackrel{{&conjugate0;}}{{z}}\right){=}\stackrel{{&conjugate0;}}{{\mathrm{sin}}\left({z}\right)}$

periodicity

 ${\mathrm{sin}}\left({2}{}{\mathrm{\pi }}{}{m}{+}{z}\right){=}{\mathrm{sin}}\left({z}\right)$ ${m}{::}{ℤ}$

 ${\mathrm{sin}}\left({\mathrm{\pi }}{}{m}{+}{z}\right){=}{\left({-1}\right)}^{{m}}{}{\mathrm{sin}}\left({z}\right)$ ${m}{::}{ℤ}$

plot

singularities

 ${\mathrm{sin}}\left({z}\right)$ ${z}{=}{\mathrm{\infty }}{+}{\mathrm{\infty }}{}{I}$

branch points

 ${\mathrm{sin}}\left({z}\right)$ No branch points

branch cuts

 ${\mathrm{sin}}\left({z}\right)$ No branch cuts

special values

 ${\mathrm{sin}}\left(\frac{{\mathrm{\pi }}}{{6}}\right){=}\frac{{1}}{{2}}$

 ${\mathrm{sin}}\left(\frac{{\mathrm{\pi }}}{{4}}\right){=}\frac{\sqrt{{2}}}{{2}}$

 ${\mathrm{sin}}\left(\frac{{\mathrm{\pi }}}{{3}}\right){=}\frac{\sqrt{{3}}}{{2}}$

 ${\mathrm{sin}}\left({\mathrm{\infty }}\right){=}{\mathrm{undefined}}$

 ${\mathrm{sin}}\left({\mathrm{\infty }}{}{I}\right){=}{\mathrm{\infty }}{}{I}$

 ${\mathrm{sin}}\left({\mathrm{\pi }}{}{n}\right){=}{0}$ ${n}{::}{ℤ}$

 ${\mathrm{sin}}\left(\frac{\left({2}{}{n}{+}{1}\right){}{\mathrm{\pi }}}{{2}}\right){=}{-1}$ ${n}{::}{\mathrm{odd}}$

 ${\mathrm{sin}}\left(\frac{\left({2}{}{n}{+}{1}\right){}{\mathrm{\pi }}}{{2}}\right){=}{1}$ ${n}{::}{\mathrm{even}}$

identities

 ${\mathrm{sin}}\left({\mathrm{arcsin}}\left({z}\right)\right){=}{z}$ ${\mathrm{sin}}\left({z}\right){=}{-}{\mathrm{sin}}\left({-}{z}\right)$ ${\mathrm{sin}}\left({z}\right){=}{2}{}{\mathrm{sin}}\left(\frac{{z}}{{2}}\right){}{\mathrm{cos}}\left(\frac{{z}}{{2}}\right)$ ${\mathrm{sin}}\left({z}\right){=}\frac{{1}}{{\mathrm{csc}}\left({z}\right)}$ ${\mathrm{sin}}\left({z}\right){=}\frac{{2}{}{\mathrm{tan}}\left(\frac{{z}}{{2}}\right)}{{1}{+}{{\mathrm{tan}}\left(\frac{{z}}{{2}}\right)}^{{2}}}$ ${\mathrm{sin}}\left({z}\right){=}{-}\frac{{I}}{{2}}{}\left({{ⅇ}}^{{I}{}{z}}{-}{{ⅇ}}^{{-I}{}{z}}\right)$ ${{\mathrm{sin}}\left({z}\right)}^{{2}}{=}{1}{-}{{\mathrm{cos}}\left({z}\right)}^{{2}}$ ${{\mathrm{sin}}\left({z}\right)}^{{2}}{=}\frac{{1}}{{2}}{-}\frac{{\mathrm{cos}}\left({2}{}{z}\right)}{{2}}$

sum form

 ${\mathrm{sin}}\left({z}\right){=}{\sum }_{{\mathrm{_k1}}{=}{0}}^{{\mathrm{\infty }}}\frac{{\left({-1}\right)}^{{\mathrm{_k1}}}{}{{z}}^{{2}{}{\mathrm{_k1}}{+}{1}}}{\left({2}{}{\mathrm{_k1}}{+}{1}\right){!}}$ ${\mathrm{with no restrictions on}}\left({z}\right)$

series

 ${\mathrm{series}}\left({\mathrm{sin}}\left({z}\right){,}{z}{,}{4}\right){=}{z}{-}\frac{{1}}{{6}}{}{{z}}^{{3}}{+}{O}\left({{z}}^{{5}}\right)$

integral form

 ${\mathrm{sin}}\left({z}\right){=}\frac{{z}{}\left({{\int }}_{{0}}^{{1}}{{ⅇ}}^{{2}{}{I}{}{\mathrm{_t1}}{}{z}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{\mathrm{_t1}}\right)}{{{ⅇ}}^{{I}{}{z}}}$ ${\mathrm{with no restrictions on}}\left({z}\right)$

differentiation rule

 $\frac{{ⅆ}}{{ⅆ}{z}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{sin}}\left({z}\right){=}{\mathrm{cos}}\left({z}\right)$

 $\frac{{{ⅆ}}^{{n}}}{{ⅆ}{{z}}^{{n}}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{sin}}\left({z}\right){=}{\mathrm{sin}}\left({z}{+}\frac{{n}{}{\mathrm{\pi }}}{{2}}\right)$

DE

${f}\left({z}\right){=}{\mathrm{sin}}\left({z}\right)$

 $\frac{{{ⅆ}}^{{2}}}{{ⅆ}{{z}}^{{2}}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{f}\left({z}\right){=}{-}{f}\left({z}\right)$

To get a Maple table structure with this same information use the table keyword (to avoid verbosity, use the option quiet)

 > $\mathrm{sin_info}≔\mathrm{FunctionAdvisor}\left(\mathrm{table},\mathrm{sin},\mathrm{quiet}\right)$
 ${\mathrm{sin_info}}{≔}{table}\left(\left[{"definition"}{=}\left[{\mathrm{sin}}\left({z}\right){=}{-}\frac{{I}}{{2}}{}\left({{ⅇ}}^{{I}{}{z}}{-}\frac{{1}}{{{ⅇ}}^{{I}{}{z}}}\right){,}{\mathrm{with no restrictions on}}\left({z}\right)\right]{,}{"classify_function"}{=}\left({\mathrm{trig}}{,}{\mathrm{elementary}}\right){,}{"branch_points"}{=}\left[{\mathrm{sin}}\left({z}\right){,}{"No branch points"}\right]{,}{"symmetries"}{=}\left[{\mathrm{sin}}\left({-}{z}\right){=}{-}{\mathrm{sin}}\left({z}\right){,}{\mathrm{sin}}\left(\stackrel{{&conjugate0;}}{{z}}\right){=}\stackrel{{&conjugate0;}}{{\mathrm{sin}}\left({z}\right)}\right]{,}{"differentiation_rule"}{=}\left(\frac{{ⅆ}}{{ⅆ}{z}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{sin}}\left({z}\right){=}{\mathrm{cos}}\left({z}\right){,}\frac{{{ⅆ}}^{{n}}}{{ⅆ}{{z}}^{{n}}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{sin}}\left({z}\right){=}{\mathrm{sin}}\left({z}{+}\frac{{n}{}{\mathrm{\pi }}}{{2}}\right)\right){,}{"describe"}{=}\left({\mathrm{sin}}{=}{\mathrm{sine function}}\right){,}{"identities"}{=}\left[{\mathrm{sin}}\left({\mathrm{arcsin}}\left({z}\right)\right){=}{z}{,}{\mathrm{sin}}\left({z}\right){=}{-}{\mathrm{sin}}\left({-}{z}\right){,}{\mathrm{sin}}\left({z}\right){=}{2}{}{\mathrm{sin}}\left(\frac{{z}}{{2}}\right){}{\mathrm{cos}}\left(\frac{{z}}{{2}}\right){,}{\mathrm{sin}}\left({z}\right){=}\frac{{1}}{{\mathrm{csc}}\left({z}\right)}{,}{\mathrm{sin}}\left({z}\right){=}\frac{{2}{}{\mathrm{tan}}\left(\frac{{z}}{{2}}\right)}{{1}{+}{{\mathrm{tan}}\left(\frac{{z}}{{2}}\right)}^{{2}}}{,}{\mathrm{sin}}\left({z}\right){=}{-}\frac{{I}}{{2}}{}\left({{ⅇ}}^{{I}{}{z}}{-}{{ⅇ}}^{{-I}{}{z}}\right){,}{{\mathrm{sin}}\left({z}\right)}^{{2}}{=}{1}{-}{{\mathrm{cos}}\left({z}\right)}^{{2}}{,}{{\mathrm{sin}}\left({z}\right)}^{{2}}{=}\frac{{1}}{{2}}{-}\frac{{\mathrm{cos}}\left({2}{}{z}\right)}{{2}}\right]{,}{"sum_form"}{=}\left[{\mathrm{sin}}\left({z}\right){=}{\sum }_{{\mathrm{_k1}}{=}{0}}^{{\mathrm{\infty }}}\frac{{\left({-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[{\mathrm{sin}}\left({z}\right){=}\frac{{z}{}\left({{\int }}_{{0}}^{{1}}{{ⅇ}}^{{2}{}{I}{}{\mathrm{_t1}}{}{z}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{\mathrm{_t1}}\right)}{{{ⅇ}}^{{I}{}{z}}}{,}{\mathrm{with no restrictions on}}\left({z}\right)\right]{,}{"special_values"}{=}\left[{\mathrm{sin}}\left(\frac{{\mathrm{\pi }}}{{6}}\right){=}\frac{{1}}{{2}}{,}{\mathrm{sin}}\left(\frac{{\mathrm{\pi }}}{{4}}\right){=}\frac{\sqrt{{2}}}{{2}}{,}{\mathrm{sin}}\left(\frac{{\mathrm{\pi }}}{{3}}\right){=}\frac{\sqrt{{3}}}{{2}}{,}{\mathrm{sin}}\left({\mathrm{\infty }}\right){=}{\mathrm{undefined}}{,}{\mathrm{sin}}\left({\mathrm{\infty }}{}{I}\right){=}{\mathrm{\infty }}{}{I}{,}\left[{\mathrm{sin}}\left({\mathrm{\pi }}{}{n}\right){=}{0}{,}{\wedge }\left({n}{::}{ℤ}\right)\right]{,}\left[{\mathrm{sin}}\left(\frac{\left({2}{}{n}{+}{1}\right){}{\mathrm{\pi }}}{{2}}\right){=}{-1}{,}{\wedge }\left({n}{::}{\mathrm{odd}}\right)\right]{,}\left[{\mathrm{sin}}\left(\frac{\left({2}{}{n}{+}{1}\right){}{\mathrm{\pi }}}{{2}}\right){=}{1}{,}{\wedge }\left({n}{::}{\mathrm{even}}\right)\right]\right]{,}{"calling_sequence"}{=}{\mathrm{sin}}\left({z}\right){,}{"periodicity"}{=}\left[\left[{\mathrm{sin}}\left({2}{}{\mathrm{\pi }}{}{m}{+}{z}\right){=}{\mathrm{sin}}\left({z}\right){,}{\wedge }\left({m}{::}{ℤ}\right)\right]{,}\left[{\mathrm{sin}}\left({\mathrm{\pi }}{}{m}{+}{z}\right){=}{\left({-1}\right)}^{{m}}{}{\mathrm{sin}}\left({z}\right){,}{\wedge }\left({m}{::}{ℤ}\right)\right]\right]{,}{"asymptotic_expansion"}{=}\left(\right){,}{"series"}{=}\left({\mathrm{series}}\left({\mathrm{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){=}{\mathrm{sin}}\left({z}\right){,}\left[\frac{{{ⅆ}}^{{2}}}{{ⅆ}{{z}}^{{2}}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{f}\left({z}\right){=}{-}{f}\left({z}\right)\right]\right]{,}{"branch_cuts"}{=}\left[{\mathrm{sin}}\left({z}\right){,}{"No branch cuts"}\right]{,}{"singularities"}{=}\left[{\mathrm{sin}}\left({z}\right){,}{z}{=}{\mathrm{\infty }}{+}{\mathrm{\infty }}{}{I}\right]\right]\right)$ (1)

You can now access the information indexing with the FunctionAdvisor topics

 > $\mathrm{sin_info}\left["differentiation_rule"\right]$
 $\frac{{ⅆ}}{{ⅆ}{z}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{sin}}\left({z}\right){=}{\mathrm{cos}}\left({z}\right){,}\frac{{{ⅆ}}^{{n}}}{{ⅆ}{{z}}^{{n}}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{sin}}\left({z}\right){=}{\mathrm{sin}}\left({z}{+}\frac{{n}{}{\mathrm{\pi }}}{{2}}\right)$ (2)

Compatibility

 • The FunctionAdvisor/table command was introduced in Maple 2016.