### The Maxima on-line user's manual

Algebra 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>.

```          (%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) ```

### Related Examples

##### residue-sin

residue (1/z, z, 0);

residue (sin(a*x)/x*...

Calculate

##### residue

residue (1/(1-E**(-z)...

Calculate

##### residue

residue(1/(s^2-a^2),s...

Calculate

##### residue-sin

residue (1/((z**2-1)*...

residue (sin(a*x)/x*...

Calculate

##### residue-sin

residue (e**z, z, 0);

residue (sin(a*x)/x*...

residue ((2*x+1)/(x*(...

Calculate

##### residue

residue ((ln(x))^2/(1...

Calculate

##### residue-sin

residue (sin(z)/(z*z^...

Calculate

##### residue-sin

residue (s/(s**2+a**2...

residue (sin(a*x)/x*...

residue ((1/a(a+p))^0...

Calculate

##### residue

residue((1-z1)/(1-z1*...

residue( (3-2*z1-2*z2...

%o2;

Calculate

##### residue

residue((z-v)^(-3)*(v...

Calculate