 FunctionAdvisor/definition - Maple Programming Help

return the definition of a given mathematical function

Parameters

 definition - literal name; 'definition' math_function - Maple name of mathematical function

Description

 • The FunctionAdvisor(definition, math_function) command returns the definition of the function used by the Maple system. This definition is typically in terms of infinite sums or integrals and sometimes in terms of other simpler functions.

Examples

 > $\mathrm{FunctionAdvisor}\left(\mathrm{definition},\mathrm{exp}\right)$
 $\left[{{ⅇ}}^{{z}}{=}{\sum }_{{\mathrm{_k1}}{=}{0}}^{{\mathrm{\infty }}}{}\frac{{{z}}^{{\mathrm{_k1}}}}{{\mathrm{_k1}}{!}}{,}{\mathrm{with no restrictions on}}{}\left({z}\right)\right]$ (1)
 > $\mathrm{FunctionAdvisor}\left(\mathrm{definition},\mathrm{arccoth}\right)$
 $\left[{\mathrm{arccoth}}{}\left({z}\right){=}\frac{{\mathrm{ln}}{}\left({z}{+}{1}\right)}{{2}}{-}\frac{{\mathrm{ln}}{}\left({z}{-}{1}\right)}{{2}}{,}{\mathrm{with no restrictions on}}{}\left({z}\right)\right]$ (2)
 > $\mathrm{FunctionAdvisor}\left(\mathrm{describe},\mathrm{arccoth}\right)$
 ${\mathrm{arccoth}}{=}{\mathrm{inverse hyperbolic cotangent function}}$ (3)
 > $\mathrm{FunctionAdvisor}\left(\mathrm{definition},\mathrm{Β}\right)$
 $\left[{\mathrm{Β}}{}\left({x}{,}{y}\right){=}\frac{{\mathrm{\Gamma }}{}\left({x}\right){}{\mathrm{\Gamma }}{}\left({y}\right)}{{\mathrm{\Gamma }}{}\left({x}{+}{y}\right)}{,}{x}{::}\left({¬}{'}{\mathrm{nonposint}}{'}\right){\wedge }{y}{::}\left({¬}{'}{\mathrm{nonposint}}{'}\right){\wedge }\left({x}{+}{y}\right){::}\left({¬}{'}{\mathrm{nonposint}}{'}\right)\right]$ (4)

The variables used by the FunctionAdvisor command to create the function calling sequences are local variables. Therefore, the previous example does not depend on z.

 > $\mathrm{depends}\left(,a\right),\mathrm{depends}\left(,z\right)$
 ${\mathrm{false}}{,}{\mathrm{false}}$ (5)

To make the FunctionAdvisor command return results using global variables, pass the function call itself when requesting the function definition.

 > $\mathrm{FunctionAdvisor}\left(\mathrm{definition},\mathrm{Β}\left(a,z\right)\right)$
 $\left[{\mathrm{Β}}{}\left({a}{,}{z}\right){=}\frac{{\mathrm{\Gamma }}{}\left({a}\right){}{\mathrm{\Gamma }}{}\left({z}\right)}{{\mathrm{\Gamma }}{}\left({a}{+}{z}\right)}{,}{a}{::}\left({¬}{'}{\mathrm{nonposint}}{'}\right){\wedge }{z}{::}\left({¬}{'}{\mathrm{nonposint}}{'}\right){\wedge }\left({a}{+}{z}\right){::}\left({¬}{'}{\mathrm{nonposint}}{'}\right)\right]$ (6)
 > $\mathrm{depends}\left(,a\right),\mathrm{depends}\left(,z\right)$
 ${\mathrm{true}}{,}{\mathrm{true}}$ (7)