MathematicalFunctions - Maple Programming Help

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MathematicalFunctions

 Get
 return information on a mathematical function

 Calling Sequence Get(topic, math_function, all)

Parameters

 topic - name; specifies the topic for information math_function - name; mathematical function all - (optional) literal name; can be used with only calling_sequence topic to return all known calling sequences

Description

 • The Get(topic, math_function) function returns the topic information on the function math_function. If the requested information is not available it returns NULL.
 • The topic argument must be one of:

 • The Get(topic, math_function) function is equivalent to FunctionAdvisor(topic, math_function), but does not attempt to match misspelled topic or math_function arguments to the correct names. For more information, see FunctionAdvisor.

Examples

 > $\mathrm{with}\left(\mathrm{MathematicalFunctions}\right)$
 $\left[{\mathrm{&Intersect}}{,}{\mathrm{&Minus}}{,}{\mathrm{&Union}}{,}{\mathrm{Assume}}{,}{\mathrm{Coulditbe}}{,}{\mathrm{Evalf}}{,}{\mathrm{Get}}{,}{\mathrm{Is}}{,}{\mathrm{SearchFunction}}{,}{\mathrm{Sequences}}{,}{\mathrm{Series}}\right]$ (1)
 > $\mathrm{Get}\left(\mathrm{series},\mathrm{arcsin}\right)$
 ${\mathrm{series}}{}\left({\mathrm{arcsin}}{}\left({z}\right){,}{z}{,}{4}\right){=}{z}{+}\frac{{1}}{{6}}{}{{z}}^{{3}}{+}{\mathrm{O}}\left({{z}}^{{5}}\right)$ (2)
 > $\mathrm{Get}\left(\mathrm{sum_form},\mathrm{tan}\right)$
 $\left[{\mathrm{tan}}{}\left({z}\right){=}{\sum }_{{\mathrm{_k1}}{=}{1}}^{{\mathrm{∞}}}\phantom{\rule[-0.0ex]{5.0px}{0.0ex}}\frac{{\mathrm{bernoulli}}{}\left({2}{}{\mathrm{_k1}}\right){}{\left({-}{1}\right)}^{{\mathrm{_k1}}}{}{{z}}^{{-}{1}{+}{2}{}{\mathrm{_k1}}}{}\left({{4}}^{{\mathrm{_k1}}}{-}{{16}}^{{\mathrm{_k1}}}\right)}{{\mathrm{Γ}}{}\left({2}{}{\mathrm{_k1}}{+}{1}\right)}{,}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{And}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\left|{z}\right|{<}\frac{{\mathrm{\pi }}}{{2}}\right]$ (3)
 > $\mathrm{Get}\left(\mathrm{special_values},\mathrm{sec}\right)$
 $\left[{\mathrm{sec}}{}\left(\frac{{1}}{{6}}{}{\mathrm{π}}\right){=}\frac{{2}}{{3}}{}\sqrt{{3}}{,}{\mathrm{sec}}{}\left(\frac{{1}}{{4}}{}{\mathrm{π}}\right){=}\sqrt{{2}}{,}{\mathrm{sec}}{}\left(\frac{{1}}{{3}}{}{\mathrm{π}}\right){=}{2}{,}{\mathrm{sec}}{}\left({\mathrm{∞}}\right){=}{\mathrm{undefined}}{,}{\mathrm{sec}}{}\left({\mathrm{∞}}{}{I}\right){=}{0}{,}\left[{\mathrm{sec}}{}\left({\mathrm{π}}{}{n}\right){=}{-}{1}{,}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{And}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{n}{::}{\mathrm{odd}}\right]{,}\left[{\mathrm{sec}}{}\left({\mathrm{π}}{}{n}\right){=}{1}{,}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{And}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{n}{::}{\mathrm{even}}\right]{,}\left[{\mathrm{sec}}{}\left(\frac{{1}}{{2}}{}{\mathrm{π}}{}{n}\right){=}{\mathrm{∞}}{+}{\mathrm{∞}}{}{I}{,}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{And}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{n}{::}{\mathrm{odd}}\right]\right]$ (4)
 > $\mathrm{Get}\left(\mathrm{branch_cuts},\mathrm{arccot}\right)$
 $\left[{\mathrm{arccot}}{}\left({z}\right){,}{z}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{∈}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathrm{ComplexRange}}{}\left({-}{\mathrm{∞}}{}{I}{,}{-}{I}\right){,}{z}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{∈}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathrm{ComplexRange}}{}\left({I}{,}{\mathrm{∞}}{}{I}\right)\right]$ (5)
 > $\mathrm{Get}\left(\mathrm{identities},\mathrm{BesselK}\right)$
 $\left[\left[{\mathrm{BesselK}}{}\left({a}{,}{I}{}{z}\right){=}{-}\frac{{1}}{{2}}{}\frac{{\mathrm{π}}{}{\mathrm{BesselY}}{}\left({a}{,}{z}\right)}{{{I}}^{{a}}}{+}\frac{{\mathrm{BesselJ}}{}\left({a}{,}{z}\right){}\left({\mathrm{ln}}{}\left({z}\right){-}{\mathrm{ln}}{}\left({I}{}{z}\right)\right)}{{{I}}^{{a}}}{,}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{And}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{a}{::}{\mathrm{integer}}\right]{,}\left[{\mathrm{BesselK}}{}\left({a}{,}{I}{}{z}\right){=}{-}\frac{{1}}{{2}}{}\frac{{\mathrm{π}}{}{{z}}^{{a}}{}{\mathrm{BesselY}}{}\left({a}{,}{z}\right)}{{\left({I}{}{z}\right)}^{{a}}}{+}\frac{{1}}{{2}}{}{\mathrm{π}}{}{\mathrm{BesselJ}}{}\left({a}{,}{z}\right){}\left({-}\frac{{\left({I}{}{z}\right)}^{{a}}}{{{z}}^{{a}}}{+}\frac{{{z}}^{{a}}{}{\mathrm{cos}}{}\left({\mathrm{π}}{}{a}\right)}{{\left({I}{}{z}\right)}^{{a}}}\right){}{\mathrm{csc}}{}\left({\mathrm{π}}{}{a}\right){,}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{And}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{a}{::}{\mathbf{Not}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathrm{integer}}\right]{,}\left[{\mathrm{BesselK}}{}\left({a}{,}{-}{z}\right){=}{\left({-}{1}\right)}^{{a}}{}{\mathrm{BesselK}}{}\left({a}{,}{z}\right){+}{\mathrm{BesselI}}{}\left({a}{,}{z}\right){}\left({\mathrm{ln}}{}\left({z}\right){-}{\mathrm{ln}}{}\left({-}{z}\right)\right){,}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{And}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{a}{::}{\mathrm{integer}}\right]{,}\left[{\mathrm{BesselK}}{}\left({a}{,}{-}{z}\right){=}\frac{{{z}}^{{a}}{}{\mathrm{BesselK}}{}\left({a}{,}{z}\right)}{{\left({-}{z}\right)}^{{a}}}{+}\frac{{1}}{{2}}{}{\mathrm{π}}{}\left(\frac{{{z}}^{{a}}}{{\left({-}{z}\right)}^{{a}}}{-}\frac{{\left({-}{z}\right)}^{{a}}}{{{z}}^{{a}}}\right){}{\mathrm{BesselI}}{}\left({a}{,}{z}\right){}{\mathrm{csc}}{}\left({\mathrm{π}}{}{a}\right){,}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{And}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{a}{::}{\mathbf{Not}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathrm{integer}}\right]{,}\left[{\mathrm{BesselK}}{}\left({a}{,}{b}{}{\left({c}{}{{z}}^{{q}}\right)}^{{p}}\right){=}\frac{{\left({b}{}{{c}}^{{p}}{}{{z}}^{{p}{}{q}}\right)}^{{a}}{}{\mathrm{BesselK}}{}\left({a}{,}{b}{}{{c}}^{{p}}{}{{z}}^{{p}{}{q}}\right)}{{\left({b}{}{\left({c}{}{{z}}^{{q}}\right)}^{{p}}\right)}^{{a}}}{-}\frac{{1}}{{2}}{}{\mathrm{π}}{}{\mathrm{csc}}{}\left({\mathrm{π}}{}{a}\right){}{\mathrm{BesselI}}{}\left({a}{,}{b}{}{{c}}^{{p}}{}{{z}}^{{p}{}{q}}\right){}\left(\frac{{\left({b}{}{\left({c}{}{{z}}^{{q}}\right)}^{{p}}\right)}^{{a}}}{{\left({b}{}{{c}}^{{p}}{}{{z}}^{{p}{}{q}}\right)}^{{a}}}{-}\frac{{\left({b}{}{{c}}^{{p}}{}{{z}}^{{p}{}{q}}\right)}^{{a}}}{{\left({b}{}{\left({c}{}{{z}}^{{q}}\right)}^{{p}}\right)}^{{a}}}\right){,}{a}{::}{\mathbf{Not}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathrm{integer}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{And}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}{}{p}{::}{\mathrm{integer}}\right]{,}\left[{\mathrm{BesselK}}{}\left({a}{,}{b}{}{\left({c}{}{{z}}^{{q}}\right)}^{{p}}\right){=}{\left(\frac{{\left({c}{}{{z}}^{{q}}\right)}^{{p}}}{{{c}}^{{p}}{}{{z}}^{{p}{}{q}}}\right)}^{{a}}{}\left({\mathrm{BesselK}}{}\left({a}{,}{b}{}{{c}}^{{p}}{}{{z}}^{{p}{}{q}}\right){-}{\left({-}{1}\right)}^{{a}}{}{\mathrm{BesselI}}{}\left({a}{,}{b}{}{{c}}^{{p}}{}{{z}}^{{p}{}{q}}\right){}\left({\mathrm{ln}}{}\left({b}{}{\left({c}{}{{z}}^{{q}}\right)}^{{p}}\right){-}{\mathrm{ln}}{}\left({b}{}{{c}}^{{p}}{}{{z}}^{{p}{}{q}}\right)\right)\right){,}{a}{::}{\mathrm{integer}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{And}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{2}{}{p}{::}{\mathrm{integer}}\right]{,}{\mathrm{BesselK}}{}\left({a}{,}{z}\right){=}\frac{{2}{}\left({a}{-}{1}\right){}{\mathrm{BesselK}}{}\left({a}{-}{1}{,}{z}\right)}{{z}}{+}{\mathrm{BesselK}}{}\left({a}{-}{2}{,}{z}\right){,}{\mathrm{BesselK}}{}\left({a}{,}{z}\right){=}{-}\frac{{2}{}\left({a}{+}{1}\right){}{\mathrm{BesselK}}{}\left({a}{+}{1}{,}{z}\right)}{{z}}{+}{\mathrm{BesselK}}{}\left({a}{+}{2}{,}{z}\right)\right]$ (6)
 > $\mathrm{Get}\left(\mathrm{calling_sequence},\mathrm{ζ},\mathrm{all}\right)$
 ${\mathrm{ζ}}{}\left({s}\right){,}{\mathrm{ζ}}{}\left({n}{,}{s}\right){,}{\mathrm{ζ}}{}\left({n}{,}{s}{,}{a}\right)$ (7)
 > $\mathrm{Get}\left(\mathrm{definition},\mathrm{JacobiAM}\right)$
 $\left[{z}{=}{\mathrm{JacobiAM}}{}\left({{∫}}_{{0}}^{{z}}\frac{{1}}{\sqrt{{1}{-}{{k}}^{{2}}{}{{\mathrm{sin}}{}\left({\mathrm{θ}}\right)}^{{2}}}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{\mathrm{θ}}{,}{k}\right){,}{z}{::}\left({\mathrm{RealRange}}{}\left({-}\frac{{3}}{{2}}{,}\frac{{3}}{{2}}\right)\right)\right]$ (8)
 > $\mathrm{Get}\left(\mathrm{definition},\mathrm{InverseJacobiAM}\right)$
 $\left[{\mathrm{InverseJacobiAM}}{}\left({\mathrm{φ}}{,}{k}\right){=}{{∫}}_{{0}}^{{\mathrm{φ}}}\frac{{1}}{\sqrt{{1}{-}{{k}}^{{2}}{}{{\mathrm{sin}}{}\left({\mathrm{_θ1}}\right)}^{{2}}}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{\mathrm{_θ1}}{,}{\mathrm{with no restrictions on}}{}\left({\mathrm{φ}}{,}{k}\right)\right]$ (9)
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