residue - Maple Programming Help

residue

compute the algebraic residue of an expression

 Calling Sequence residue(f, x=a)

Parameters

 f - arbitrary algebraic expression x - variable a - algebraic value at which the residue is evaluated

Description

 • Computes the algebraic residue of the expression f for the variable x around the point a. The residue is defined as the coefficient of $\frac{1}{x-a}$ in the Laurent series expansion of f.

Examples

 > $\mathrm{residue}\left(\mathrm{ζ}\left(s\right),s=1\right)$
 ${1}$ (1)
 > $\mathrm{residue}\left(\frac{\mathrm{Ψ}\left(x\right)\mathrm{Γ}\left(x\right)}{x},x=0\right)$
 $\frac{{1}}{{12}}{}{{\mathrm{π}}}^{{2}}{+}\frac{{1}}{{2}}{}{{\mathrm{γ}}}^{{2}}$ (2)
 > $\mathrm{residue}\left({ⅇ}^{x},x=1\right)$
 ${0}$ (3)