FunctionAdvisor/known_functions - Maple Programming Help

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FunctionAdvisor/known_functions

return a list of the mathematical function's names known by FunctionAdvisor

 Calling Sequence FunctionAdvisor(known_functions)

Parameters

 known_functions - literal name; 'known_functions'

Description

 • The FunctionAdvisor(known_functions) command returns a list of the mathematical function's names implemented in the Maple system.

Examples

 > $\mathrm{FunctionAdvisor}\left(\mathrm{known_functions}\right)$
 The functions on which information is available via     > FunctionAdvisor( function_name ); are:
 $\left[{\mathrm{AiryAi}}{,}{\mathrm{AiryBi}}{,}{\mathrm{AngerJ}}{,}{\mathrm{AppellF1}}{,}{\mathrm{AppellF2}}{,}{\mathrm{AppellF3}}{,}{\mathrm{AppellF4}}{,}{\mathrm{BellB}}{,}{\mathrm{BesselI}}{,}{\mathrm{BesselJ}}{,}{\mathrm{BesselK}}{,}{\mathrm{BesselY}}{,}{\mathrm{Β}}{,}{\mathrm{ChebyshevT}}{,}{\mathrm{ChebyshevU}}{,}{\mathrm{Chi}}{,}{\mathrm{Ci}}{,}{\mathrm{CoulombF}}{,}{\mathrm{CylinderD}}{,}{\mathrm{CylinderU}}{,}{\mathrm{CylinderV}}{,}{\mathrm{Dirac}}{,}{\mathrm{Ei}}{,}{\mathrm{EllipticCE}}{,}{\mathrm{EllipticCK}}{,}{\mathrm{EllipticCPi}}{,}{\mathrm{EllipticE}}{,}{\mathrm{EllipticF}}{,}{\mathrm{EllipticK}}{,}{\mathrm{EllipticModulus}}{,}{\mathrm{EllipticNome}}{,}{\mathrm{EllipticPi}}{,}{\mathrm{FresnelC}}{,}{\mathrm{FresnelS}}{,}{\mathrm{Fresnelf}}{,}{\mathrm{Fresnelg}}{,}{\mathrm{\Gamma }}{,}{\mathrm{GaussAGM}}{,}{\mathrm{GegenbauerC}}{,}{\mathrm{GeneralizedPolylog}}{,}{\mathrm{HankelH1}}{,}{\mathrm{HankelH2}}{,}{\mathrm{Heaviside}}{,}{\mathrm{HermiteH}}{,}{\mathrm{HeunB}}{,}{\mathrm{HeunBPrime}}{,}{\mathrm{HeunC}}{,}{\mathrm{HeunCPrime}}{,}{\mathrm{HeunD}}{,}{\mathrm{HeunDPrime}}{,}{\mathrm{HeunG}}{,}{\mathrm{HeunGPrime}}{,}{\mathrm{HeunT}}{,}{\mathrm{HeunTPrime}}{,}{\mathrm{Hypergeom}}{,}{\mathrm{\Im }}{,}{\mathrm{InverseJacobiAM}}{,}{\mathrm{InverseJacobiCD}}{,}{\mathrm{InverseJacobiCN}}{,}{\mathrm{InverseJacobiCS}}{,}{\mathrm{InverseJacobiDC}}{,}{\mathrm{InverseJacobiDN}}{,}{\mathrm{InverseJacobiDS}}{,}{\mathrm{InverseJacobiNC}}{,}{\mathrm{InverseJacobiND}}{,}{\mathrm{InverseJacobiNS}}{,}{\mathrm{InverseJacobiSC}}{,}{\mathrm{InverseJacobiSD}}{,}{\mathrm{InverseJacobiSN}}{,}{\mathrm{JacobiAM}}{,}{\mathrm{JacobiCD}}{,}{\mathrm{JacobiCN}}{,}{\mathrm{JacobiCS}}{,}{\mathrm{JacobiDC}}{,}{\mathrm{JacobiDN}}{,}{\mathrm{JacobiDS}}{,}{\mathrm{JacobiNC}}{,}{\mathrm{JacobiND}}{,}{\mathrm{JacobiNS}}{,}{\mathrm{JacobiP}}{,}{\mathrm{JacobiSC}}{,}{\mathrm{JacobiSD}}{,}{\mathrm{JacobiSN}}{,}{\mathrm{JacobiTheta1}}{,}{\mathrm{JacobiTheta2}}{,}{\mathrm{JacobiTheta3}}{,}{\mathrm{JacobiTheta4}}{,}{\mathrm{JacobiZeta}}{,}{\mathrm{KelvinBei}}{,}{\mathrm{KelvinBer}}{,}{\mathrm{KelvinHei}}{,}{\mathrm{KelvinHer}}{,}{\mathrm{KelvinKei}}{,}{\mathrm{KelvinKer}}{,}{\mathrm{KummerM}}{,}{\mathrm{KummerU}}{,}{\mathrm{LaguerreL}}{,}{\mathrm{LambertW}}{,}{\mathrm{LegendreP}}{,}{\mathrm{LegendreQ}}{,}{\mathrm{LerchPhi}}{,}{\mathrm{Li}}{,}{\mathrm{LommelS1}}{,}{\mathrm{LommelS2}}{,}{\mathrm{MathieuA}}{,}{\mathrm{MathieuB}}{,}{\mathrm{MathieuC}}{,}{\mathrm{MathieuCE}}{,}{\mathrm{MathieuCEPrime}}{,}{\mathrm{MathieuCPrime}}{,}{\mathrm{MathieuExponent}}{,}{\mathrm{MathieuFloquet}}{,}{\mathrm{MathieuFloquetPrime}}{,}{\mathrm{MathieuS}}{,}{\mathrm{MathieuSE}}{,}{\mathrm{MathieuSEPrime}}{,}{\mathrm{MathieuSPrime}}{,}{\mathrm{MeijerG}}{,}{\mathrm{MultiPolylog}}{,}{\mathrm{NielsenPolylog}}{,}{\mathrm{\Psi }}{,}{\mathrm{\Re }}{,}{\mathrm{Shi}}{,}{\mathrm{Si}}{,}{\mathrm{SphericalY}}{,}{\mathrm{Ssi}}{,}{\mathrm{Stirling1}}{,}{\mathrm{Stirling2}}{,}{\mathrm{StruveH}}{,}{\mathrm{StruveL}}{,}{\mathrm{WeberE}}{,}{\mathrm{WeierstrassP}}{,}{\mathrm{WeierstrassPPrime}}{,}{\mathrm{WeierstrassSigma}}{,}{\mathrm{WeierstrassZeta}}{,}{\mathrm{WhittakerM}}{,}{\mathrm{WhittakerW}}{,}{\mathrm{Wrightomega}}{,}{\mathrm{\zeta }}{,}{\mathrm{abs}}{,}{\mathrm{arccos}}{,}{\mathrm{arccosh}}{,}{\mathrm{arccot}}{,}{\mathrm{arccoth}}{,}{\mathrm{arccsc}}{,}{\mathrm{arccsch}}{,}{\mathrm{arcsec}}{,}{\mathrm{arcsech}}{,}{\mathrm{arcsin}}{,}{\mathrm{arcsinh}}{,}{\mathrm{arctan}}{,}{\mathrm{arctanh}}{,}{\mathrm{argument}}{,}{\mathrm{bernoulli}}{,}{\mathrm{binomial}}{,}{\mathrm{conjugate}}{,}{\mathrm{cos}}{,}{\mathrm{cosh}}{,}{\mathrm{cot}}{,}{\mathrm{coth}}{,}{\mathrm{csc}}{,}{\mathrm{csch}}{,}{\mathrm{csgn}}{,}{\mathrm{dawson}}{,}{\mathrm{dilog}}{,}{\mathrm{doublefactorial}}{,}{\mathrm{erf}}{,}{\mathrm{erfc}}{,}{\mathrm{erfi}}{,}{\mathrm{euler}}{,}{\mathrm{exp}}{,}{\mathrm{factorial}}{,}{\mathrm{harmonic}}{,}{\mathrm{hypergeom}}{,}{\mathrm{ln}}{,}{\mathrm{lnGAMMA}}{,}{\mathrm{log}}{,}{\mathrm{max}}{,}{\mathrm{min}}{,}{\mathrm{piecewise}}{,}{\mathrm{pochhammer}}{,}{\mathrm{polylog}}{,}{\mathrm{sec}}{,}{\mathrm{sech}}{,}{\mathrm{signum}}{,}{\mathrm{sin}}{,}{\mathrm{sinh}}{,}{\mathrm{tan}}{,}{\mathrm{tanh}}{,}{\mathrm{unwindK}}\right]$ (1)

You can get a table of information for each function by specifying the function and the table keyword.

 > $\mathrm{info_arccot}≔\mathrm{FunctionAdvisor}\left(\mathrm{table},\mathrm{arccot}\right)$
 arccot belongs to the subclass "arctrig" of the class "elementary" and so, in principle, it can be related to various of the 26 functions of those classes - see FunctionAdvisor( "arctrig" ); and FunctionAdvisor( "elementary" );
 ${\mathrm{info_arccot}}{≔}{table}{}\left(\left[{"singularities"}{=}\left[{\mathrm{arccot}}{}\left({z}\right){,}{z}{=}{\mathrm{\infty }}{+}{\mathrm{\infty }}{}{I}\right]{,}{"periodicity"}{=}\left[{\mathrm{arccot}}{}\left({z}\right){,}{"No periodicity"}\right]{,}{"differentiation_rule"}{=}\left(\frac{{ⅆ}}{{ⅆ}{z}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{arccot}{}\left({z}\right){=}{-}\frac{{1}}{{{z}}^{{2}}{+}{1}}{,}\frac{{{ⅆ}}^{{n}}}{{ⅆ}{{z}}^{{n}}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{arccot}{}\left({z}\right){=}\left\{\begin{array}{cc}{\mathrm{arccot}}{}\left({z}\right)& {n}{=}{0}\\ {-}{{2}}^{{n}{-}{1}}{}{\mathrm{MeijerG}}{}\left(\left[\left[{0}{,}{0}{,}\frac{{1}}{{2}}\right]{,}\left[\right]\right]{,}\left[\left[{0}\right]{,}\left[{-}\frac{{1}}{{2}}{+}\frac{{n}}{{2}}{,}\frac{{n}}{{2}}\right]\right]{,}{{z}}^{{2}}\right){}{{z}}^{{1}{-}{n}}& {\mathrm{otherwise}}\end{array}\right\\right){,}{"symmetries"}{=}\left[{\mathrm{arccot}}{}\left({-}{z}\right){=}{\mathrm{\pi }}{-}{\mathrm{arccot}}{}\left({z}\right){,}\left[{\mathrm{arccot}}{}\left(\stackrel{{&conjugate0;}}{{z}}\right){=}\stackrel{{&conjugate0;}}{{\mathrm{arccot}}{}\left({z}\right)}{,}{\mathbf{not}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\left({z}{\in }{\mathrm{ComplexRange}}{}\left({-}{\mathrm{\infty }}{}{I}{,}{-I}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{\mathbf{or}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{z}{\in }{\mathrm{ComplexRange}}{}\left({I}{,}{\mathrm{\infty }}{}{I}\right)\right)\right]\right]{,}{"calling_sequence"}{=}{\mathrm{arccot}}{}\left({z}\right){,}{"integral_form"}{=}\left[{\mathrm{arccot}}{}\left({z}\right){=}{{\int }}_{{1}{+}{I}{}{z}}^{{1}{-}{I}{}{z}}\frac{{-}\frac{{I}}{{2}}}{{\mathrm{_k1}}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{\mathrm{_k1}}{+}\frac{{\mathrm{\pi }}}{{2}}{,}{\mathrm{with no restrictions on}}{}\left({z}\right)\right]{,}{"series"}{=}\left({\mathrm{series}}{}\left({\mathrm{arccot}}{}\left({z}\right){,}{z}{,}{4}\right){=}\frac{{\mathrm{\pi }}}{{2}}{-}{z}{+}\frac{{1}}{{3}}{}{{z}}^{{3}}{+}{O}{}\left({{z}}^{{5}}\right)\right){,}{"branch_cuts"}{=}\left[{\mathrm{arccot}}{}\left({z}\right){,}{z}{\in }{\mathrm{ComplexRange}}{}\left({-}{\mathrm{\infty }}{}{I}{,}{-I}\right){\vee }{z}{\in }{\mathrm{ComplexRange}}{}\left({I}{,}{\mathrm{\infty }}{}{I}\right)\right]{,}{"identities"}{=}\left[{\mathrm{cot}}{}\left({\mathrm{arccot}}{}\left({z}\right)\right){=}{z}{,}{\mathrm{cot}}{}\left({\mathrm{arccot}}{}\left({z}\right){+}{\mathrm{arccot}}{}\left({y}\right)\right){=}\frac{{y}{}{z}{-}{1}}{{z}{+}{y}}\right]{,}{"classify_function"}{=}\left({\mathrm{arctrig}}{,}{\mathrm{elementary}}\right){,}{"asymptotic_expansion"}{=}\left({\mathrm{asympt}}{}\left({\mathrm{arccot}}{}\left({z}\right){,}{z}{,}{4}\right){=}\frac{{1}}{{z}}{-}\frac{{1}}{{3}{}{{z}}^{{3}}}{+}{\mathrm{O}}{}\left(\frac{{1}}{{{z}}^{{5}}}\right)\right){,}{"DE"}{=}\left[{f}{}\left({z}\right){=}{\mathrm{arccot}}{}\left({z}\right){,}\left[\frac{{ⅆ}}{{ⅆ}{z}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{f}{}\left({z}\right){=}{-}\frac{{1}}{{{z}}^{{2}}{+}{1}}\right]\right]{,}{"sum_form"}{=}\left[{\mathrm{arccot}}{}\left({z}\right){=}{\sum }_{{\mathrm{_k1}}{=}{0}}^{{\mathrm{\infty }}}{}\left({-}\frac{{z}{}\left({\left({I}{}{z}\right)}^{{\mathrm{_k1}}}{+}{\left({-I}{}{z}\right)}^{{\mathrm{_k1}}}\right)}{{2}{}{\mathrm{_k1}}{+}{2}}\right){+}\frac{{\mathrm{\pi }}}{{2}}{,}{?}\right]{,}{"describe"}{=}\left({\mathrm{arccot}}{=}{\mathrm{inverse cotangent function}}\right){,}{"definition"}{=}\left[{\mathrm{arccot}}{}\left({z}\right){=}\frac{{\mathrm{\pi }}}{{2}}{-}\frac{{I}{}\left({\mathrm{ln}}{}\left({1}{-}{I}{}{z}\right){-}{\mathrm{ln}}{}\left({1}{+}{I}{}{z}\right)\right)}{{2}}{,}{\mathrm{with no restrictions on}}{}\left({z}\right)\right]{,}{"branch_points"}{=}\left[{\mathrm{arccot}}{}\left({z}\right){,}{z}{\in }\left[{-I}{,}{I}\right]\right]{,}{"special_values"}{=}\left[{\mathrm{arccot}}{}\left({-1}\right){=}\frac{{3}{}{\mathrm{\pi }}}{{4}}{,}{\mathrm{arccot}}{}\left({-}\frac{\sqrt{{3}}}{{3}}\right){=}\frac{{2}{}{\mathrm{\pi }}}{{3}}{,}{\mathrm{arccot}}{}\left({-}\sqrt{{3}}\right){=}\frac{{5}{}{\mathrm{\pi }}}{{6}}{,}{\mathrm{arccot}}{}\left({0}\right){=}\frac{{\mathrm{\pi }}}{{2}}{,}{\mathrm{arccot}}{}\left(\sqrt{{3}}\right){=}\frac{{\mathrm{\pi }}}{{6}}{,}{\mathrm{arccot}}{}\left(\frac{\sqrt{{3}}}{{3}}\right){=}\frac{{\mathrm{\pi }}}{{3}}{,}{\mathrm{arccot}}{}\left({1}\right){=}\frac{{\mathrm{\pi }}}{{4}}{,}{\mathrm{arccot}}{}\left({\mathrm{\infty }}\right){=}{0}{,}{\mathrm{arccot}}{}\left({-}{\mathrm{\infty }}\right){=}{\mathrm{\pi }}\right]\right]\right)$ (2)
 > $\mathrm{info_arccot}\left["describe"\right]$
 ${\mathrm{arccot}}{=}{\mathrm{inverse cotangent function}}$ (3)
 > $\mathrm{info_arccot}\left["definition"\right]$
 $\left[{\mathrm{arccot}}{}\left({z}\right){=}\frac{{\mathrm{\pi }}}{{2}}{-}\frac{{I}{}\left({\mathrm{ln}}{}\left({1}{-}{I}{}{z}\right){-}{\mathrm{ln}}{}\left({1}{+}{I}{}{z}\right)\right)}{{2}}{,}{\mathrm{with no restrictions on}}{}\left({z}\right)\right]$ (4)

 See Also