display information about a mathematical function in an ordered manner - Maple Help

FunctionAdvisor/display - display information about a mathematical function in an ordered manner

 Calling Sequence FunctionAdvisor(display, math_function)

Parameters

 display - literal name; 'display' math_function - name of known mathematical function; see type/mathfunc

Description

 • The FunctionAdvisor(display, math_function) command returns the information regarding that function available to the system. The information that displays is essentially the same as what you obtain by calling the FunctionAdvisor command without the keyword display.

Examples

 > $\mathrm{sin_info}:=\mathrm{FunctionAdvisor}\left(\mathrm{sin}\right)$
 The system is unable to compute the "asymptotic_expansion" for sin sin belongs to the subclass "trig" of the class "elementary" and so, in principle, it can be related to various of the 26 functions of those classes - see FunctionAdvisor( "trig" ); and FunctionAdvisor( "elementary" );
 ${\mathrm{sin_info}}{:=}{\mathrm{table}}\left(\left[{"sum_form"}{=}\left[{\mathrm{sin}}{}\left({z}\right){=}{\sum }_{{\mathrm{_k1}}{=}{0}}^{{\mathrm{∞}}}\phantom{\rule[-0.0ex]{5.0px}{0.0ex}}\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]{,}{"identities"}{=}\left[{\mathrm{sin}}{}\left({z}\right){=}{-}{\mathrm{sin}}{}\left({-}{z}\right){,}{\mathrm{sin}}{}\left({z}\right){=}{2}{}{\mathrm{sin}}{}\left(\frac{{1}}{{2}}{}{z}\right){}{\mathrm{cos}}{}\left(\frac{{1}}{{2}}{}{z}\right){,}{\mathrm{sin}}{}\left({z}\right){=}\frac{{1}}{{\mathrm{csc}}{}\left({z}\right)}{,}{\mathrm{sin}}{}\left({z}\right){=}\frac{{2}{}{\mathrm{tan}}{}\left(\frac{{1}}{{2}}{}{z}\right)}{{1}{+}{{\mathrm{tan}}{}\left(\frac{{1}}{{2}}{}{z}\right)}^{{2}}}{,}{\mathrm{sin}}{}\left({z}\right){=}{-}\frac{{1}}{{2}}{}{I}{}\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{{1}}{{2}}{}{\mathrm{cos}}{}\left({2}{}{z}\right)\right]{,}{"differentiation_rule"}{=}\left(\frac{{ⅆ}}{{ⅆ}{z}}{}{\mathrm{sin}}{}\left({z}\right){=}{\mathrm{cos}}{}\left({z}\right)\right){,}{"series"}{=}\left({\mathrm{series}}{}\left({\mathrm{sin}}{}\left({z}\right){,}{z}{,}{4}\right){=}{z}{-}\frac{{1}}{{6}}{}{{z}}^{{3}}{+}{\mathrm{O}}\left({{z}}^{{5}}\right)\right){,}{"describe"}{=}\left({\mathrm{sin}}{=}{\mathrm{sine function}}\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]{,}{"special_values"}{=}\left[{\mathrm{sin}}{}\left(\frac{{1}}{{6}}{}{\mathrm{π}}\right){=}\frac{{1}}{{2}}{,}{\mathrm{sin}}{}\left(\frac{{1}}{{4}}{}{\mathrm{π}}\right){=}\frac{{1}}{{2}}{}\sqrt{{2}}{,}{\mathrm{sin}}{}\left(\frac{{1}}{{3}}{}{\mathrm{π}}\right){=}\frac{{1}}{{2}}{}\sqrt{{3}}{,}{\mathrm{sin}}{}\left({\mathrm{∞}}\right){=}{\mathrm{undefined}}{,}{\mathrm{sin}}{}\left({\mathrm{∞}}{}{I}\right){=}{\mathrm{∞}}{}{I}{,}\left[{\mathrm{sin}}{}\left({\mathrm{π}}{}{n}\right){=}{0}{,}{\mathrm{And}}{}\left({n}{::}{\mathrm{integer}}\right)\right]{,}\left[{\mathrm{sin}}{}\left(\frac{{1}}{{2}}{}\left({2}{}{n}{+}{1}\right){}{\mathrm{π}}\right){=}{-}{1}{,}{\mathrm{And}}{}\left({n}{::}{\mathrm{odd}}\right)\right]{,}\left[{\mathrm{sin}}{}\left(\frac{{1}}{{2}}{}\left({2}{}{n}{+}{1}\right){}{\mathrm{π}}\right){=}{1}{,}{\mathrm{And}}{}\left({n}{::}{\mathrm{even}}\right)\right]\right]{,}{"integral_form"}{=}\left[{\mathrm{sin}}{}\left({z}\right){=}\frac{{z}{}\left({{∫}}_{{0}}^{{1}}{{ⅇ}}^{{2}{}{I}{}{z}{}{\mathrm{_t1}}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{\mathrm{_t1}}\right)}{{{ⅇ}}^{{I}{}{z}}}{,}{\mathrm{with no restrictions on}}{}\left({z}\right)\right]{,}{"classify_function"}{=}\left({\mathrm{trig}}{,}{\mathrm{elementary}}\right){,}{"DE"}{=}\left[{f}{}\left({z}\right){=}{\mathrm{sin}}{}\left({z}\right){,}\left[\frac{{{ⅆ}}^{{2}}}{{ⅆ}{{z}}^{{2}}}{}{f}{}\left({z}\right){=}{-}{f}{}\left({z}\right)\right]\right]{,}{"singularities"}{=}\left[{\mathrm{sin}}{}\left({z}\right){,}{z}{=}{\mathrm{∞}}{+}{\mathrm{∞}}{}{I}\right]{,}{"calling_sequence"}{=}{\mathrm{sin}}{}\left({z}\right){,}{"asymptotic_expansion"}{=}\left({}\right){,}{"branch_cuts"}{=}\left[{\mathrm{sin}}{}\left({z}\right){,}{"No branch cuts"}\right]{,}{"definition"}{=}\left[{\mathrm{sin}}{}\left({z}\right){=}{-}\frac{{1}}{{2}}{}{I}{}\left({{ⅇ}}^{{I}{}{z}}{-}\frac{{1}}{{{ⅇ}}^{{I}{}{z}}}\right){,}{\mathrm{with no restrictions on}}{}\left({z}\right)\right]{,}{"periodicity"}{=}\left[\left[{\mathrm{sin}}{}\left({2}{}{\mathrm{π}}{}{m}{+}{z}\right){=}{\mathrm{sin}}{}\left({z}\right){,}{\mathrm{And}}{}\left({m}{::}{\mathrm{integer}}\right)\right]{,}\left[{\mathrm{sin}}{}\left({\mathrm{π}}{}{m}{+}{z}\right){=}{\left({-}{1}\right)}^{{m}}{}{\mathrm{sin}}{}\left({z}\right){,}{\mathrm{And}}{}\left({m}{::}{\mathrm{integer}}\right)\right]\right]{,}{"branch_points"}{=}\left[{\mathrm{sin}}{}\left({z}\right){,}{"No branch points"}\right]\right]\right)$ (1)
 > $\mathrm{FunctionAdvisor}\left(\mathrm{display},\mathrm{sin}\right)$
 The system is unable to compute the "asymptotic_expansion" for sin sin belongs to the subclass "trig" of the class "elementary" and so, in principle, it can be related to various of the 26 functions of those classes - see FunctionAdvisor( "trig" ); and FunctionAdvisor( "elementary" );
 ${\mathrm{describe}}{=}\left({\mathrm{sin}}{=}{\mathrm{sine function}}\right)$
 ${\mathrm{classify_function}}{=}\left({\mathrm{trig}}{,}{\mathrm{elementary}}\right)$
 ${\mathrm{definition}}{=}\left[{\mathrm{sin}}{}\left({z}\right){=}{-}\frac{{1}}{{2}}{}{I}{}\left({{ⅇ}}^{{I}{}{z}}{-}\frac{{1}}{{{ⅇ}}^{{I}{}{z}}}\right){,}{\mathrm{with no restrictions on}}{}\left({z}\right)\right]$
 ${\mathrm{symmetries}}{=}\left[{\mathrm{sin}}{}\left({-}{z}\right){=}{-}{\mathrm{sin}}{}\left({z}\right){,}{\mathrm{sin}}{}\left(\stackrel{{&conjugate0;}}{{z}}\right){=}\stackrel{{&conjugate0;}}{{\mathrm{sin}}{}\left({z}\right)}\right]$
 ${\mathrm{periodicity}}{=}\left[\left[{\mathrm{sin}}{}\left({2}{}{\mathrm{π}}{}{m}{+}{z}\right){=}{\mathrm{sin}}{}\left({z}\right){,}{\mathrm{And}}{}\left({m}{::}{\mathrm{integer}}\right)\right]{,}\left[{\mathrm{sin}}{}\left({\mathrm{π}}{}{m}{+}{z}\right){=}{\left({-}{1}\right)}^{{m}}{}{\mathrm{sin}}{}\left({z}\right){,}{\mathrm{And}}{}\left({m}{::}{\mathrm{integer}}\right)\right]\right]$
 ${\mathrm{singularities}}{=}\left[{\mathrm{sin}}{}\left({z}\right){,}{z}{=}{\mathrm{∞}}{+}{\mathrm{∞}}{}{I}\right]$
 ${\mathrm{branch_points}}{=}\left[{\mathrm{sin}}{}\left({z}\right){,}{\mathrm{No branch points}}\right]$
 ${\mathrm{branch_cuts}}{=}\left[{\mathrm{sin}}{}\left({z}\right){,}{\mathrm{No branch cuts}}\right]$
 ${\mathrm{special_values}}{=}\left[{\mathrm{sin}}{}\left(\frac{{1}}{{6}}{}{\mathrm{π}}\right){=}\frac{{1}}{{2}}{,}{\mathrm{sin}}{}\left(\frac{{1}}{{4}}{}{\mathrm{π}}\right){=}\frac{{1}}{{2}}{}\sqrt{{2}}{,}{\mathrm{sin}}{}\left(\frac{{1}}{{3}}{}{\mathrm{π}}\right){=}\frac{{1}}{{2}}{}\sqrt{{3}}{,}{\mathrm{sin}}{}\left({\mathrm{∞}}\right){=}{\mathrm{undefined}}{,}{\mathrm{sin}}{}\left({\mathrm{∞}}{}{I}\right){=}{\mathrm{∞}}{}{I}{,}\left[{\mathrm{sin}}{}\left({\mathrm{π}}{}{n}\right){=}{0}{,}{\mathrm{And}}{}\left({n}{::}{\mathrm{integer}}\right)\right]{,}\left[{\mathrm{sin}}{}\left(\frac{{1}}{{2}}{}\left({2}{}{n}{+}{1}\right){}{\mathrm{π}}\right){=}{-}{1}{,}{\mathrm{And}}{}\left({n}{::}{\mathrm{odd}}\right)\right]{,}\left[{\mathrm{sin}}{}\left(\frac{{1}}{{2}}{}\left({2}{}{n}{+}{1}\right){}{\mathrm{π}}\right){=}{1}{,}{\mathrm{And}}{}\left({n}{::}{\mathrm{even}}\right)\right]\right]$
 ${\mathrm{identities}}{=}\left[{\mathrm{sin}}{}\left({z}\right){=}{-}{\mathrm{sin}}{}\left({-}{z}\right){,}{\mathrm{sin}}{}\left({z}\right){=}{2}{}{\mathrm{sin}}{}\left(\frac{{1}}{{2}}{}{z}\right){}{\mathrm{cos}}{}\left(\frac{{1}}{{2}}{}{z}\right){,}{\mathrm{sin}}{}\left({z}\right){=}\frac{{1}}{{\mathrm{csc}}{}\left({z}\right)}{,}{\mathrm{sin}}{}\left({z}\right){=}\frac{{2}{}{\mathrm{tan}}{}\left(\frac{{1}}{{2}}{}{z}\right)}{{1}{+}{{\mathrm{tan}}{}\left(\frac{{1}}{{2}}{}{z}\right)}^{{2}}}{,}{\mathrm{sin}}{}\left({z}\right){=}{-}\frac{{1}}{{2}}{}{I}{}\left({{ⅇ}}^{{I}{}{z}}{-}{{ⅇ}}^{{-}{I}{}{z}}\right){,}{{\mathrm{sin}}{}\left({z}\right)}^{{2}}{=}{1}{-}{{\mathrm{cos}}{}\left({z}\right)}^{{2}}{,}{{\mathrm{sin}}{}\left({z}\right)}^{{2}}{=}\frac{{1}}{{2}}{-}\frac{{1}}{{2}}{}{\mathrm{cos}}{}\left({2}{}{z}\right)\right]$
 ${\mathrm{sum_form}}{=}\left[{\mathrm{sin}}{}\left({z}\right){=}{\sum }_{{\mathrm{_k1}}{=}{0}}^{{\mathrm{∞}}}\phantom{\rule[-0.0ex]{5.0px}{0.0ex}}\frac{{\left({-}{1}\right)}^{{\mathrm{_k1}}}{}{{z}}^{{2}{}{\mathrm{_k1}}{+}{1}}}{\left({2}{}{\mathrm{_k1}}{+}{1}\right){!}}{,}{\mathrm{with no restrictions on}}{}\left({z}\right)\right]$
 ${\mathrm{series}}{=}\left({\mathrm{series}}{}\left({\mathrm{sin}}{}\left({z}\right){,}{z}{,}{4}\right){=}{z}{-}\frac{{1}}{{6}}{}{{z}}^{{3}}{+}{\mathrm{O}}\left({{z}}^{{5}}\right)\right)$
 ${\mathrm{integral_form}}{=}\left[{\mathrm{sin}}{}\left({z}\right){=}\frac{{z}{}\left({{∫}}_{{0}}^{{1}}{{ⅇ}}^{{2}{}{I}{}{z}{}{\mathrm{_t1}}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{\mathrm{_t1}}\right)}{{{ⅇ}}^{{I}{}{z}}}{,}{\mathrm{with no restrictions on}}{}\left({z}\right)\right]$
 ${\mathrm{differentiation_rule}}{=}\left(\frac{{ⅆ}}{{ⅆ}{z}}{}{\mathrm{sin}}{}\left({z}\right){=}{\mathrm{cos}}{}\left({z}\right)\right)$
 ${\mathrm{DE}}{=}\left[{f}{}\left({z}\right){=}{\mathrm{sin}}{}\left({z}\right){,}\left[\frac{{{ⅆ}}^{{2}}}{{ⅆ}{{z}}^{{2}}}{}{f}{}\left({z}\right){=}{-}{f}{}\left({z}\right)\right]\right]$ (2)
 > 

Because you defined sin_info, the call FunctionAdvisor(display, sin_info) is also a valid and produces the same presentation as FunctionAdvisor(display, sin).