FunctionAdvisor/analytic_extension - Maple Programming Help

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FunctionAdvisor/analytic_extension

return the definition of the analytic extension of a given mathematical function

 Calling Sequence FunctionAdvisor(analytic_extension, math_function)

Parameters

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

Description

 • The FunctionAdvisor(analytic_extension, math_function) command returns the definition of the analytic extension used by Maple to extend the function outside the classical domain, typically to the entire complex plane.
 Note: For most functions the domain of the classical definition is the entire complex plane. If the requested information is not available, the FunctionAdvisor command returns NULL.

Examples

 > $\mathrm{FunctionAdvisor}\left(\mathrm{definition},\mathrm{Γ}\left(z\right)\right)$
 $\left[{\mathrm{Γ}}{}\left({z}\right){=}{{∫}}_{{0}}^{{\mathrm{∞}}}\frac{{{\mathrm{_k1}}}^{{z}{-}{1}}}{{{ⅇ}}^{{\mathrm{_k1}}}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{\mathrm{_k1}}{,}{\mathrm{And}}{}\left({0}{<}{\mathrm{ℜ}}{}\left({z}\right)\right)\right]$ (1)
 > $\mathrm{FunctionAdvisor}\left(\mathrm{analytic_extension},\mathrm{Γ}\right)$
 ${\mathrm{Γ}}{}\left({z}\right){=}\frac{{\mathrm{π}}}{{\mathrm{sin}}{}\left({\mathrm{π}}{}{z}\right){}{\mathrm{Γ}}{}\left({1}{-}{z}\right)}{,}{\mathrm{And}}{}\left({\mathrm{ℜ}}{}\left({z}\right){<}{0}\right)$ (2)

 See Also

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