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The Maxima on-line user's manual

Algebra Calculator

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Residue Calculator

Residue

Function: residue (<expr>, <z>, <z_0>) Computes the residue in the complex plane of the expression <expr> when the variable <z> assumes the value <z_0>. The residue is the coefficient of (<z> - <z_0>)^(-1) in the Laurent series for <expr>.

residue (x^3*cos(x), x, 0);

          (%i1) residue (s/(s**2+a**2), s, a*%i);
                                          1
          (%o1)                           -
                                          2
          (%i2) residue (sin(a*x)/x**4, x, 0);
                                           3
                                          a
          (%o2)                         - --
                                          6

(%o1)                                true
(%i2) 

Residue Example

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