# The residue of an expression at a point: residue

### 5.36.4 The residue of an expression at a point: residue

The residue command finds the residue of an expression at a point.

- residue takes three arguments:
  - expr, an expression depending on a variable.
  - x, a variable name.
  - a, a complex number. This can be combined with the previous argument in an equality x=a.
- residue(expr,x,a) returns the residue of expr at the point a.

#### Example.

Input:

residue(cos(x)/x^3,x,0)

or:

residue(cos(x)/x^3,x=0)

Output:

−

1
2