# poles

Poles of expression or function

## Description

example

P = poles(f,var) finds the poles of f with respect to variable var.

example

P = poles(f,var,a,b) returns poles in the interval (a,b).

example

[P,N] = poles(___) returns the poles of f and their orders in N.

example

[P,N,R] = poles(___) returns the poles of f, their orders, and residues in R.

## Examples

collapse all

syms x
poles(1/(x-1i))
ans =
1i
poles(sin(x)/(x-1))
ans =
1

Find the poles of this expression. If you do not specify a variable, poles uses the default variable determined by symvar.

syms x a
f = 1/((x-1)*(a-2));
poles(f)
ans =
1

Find the poles with respect to a by specifying the second argument.

syms x a
poles(f,a)
ans =
2

Find the poles of the tangent function in the interval (-pi, pi).

syms x
poles(tan(x), x, -pi, pi)
ans =
-pi/2
pi/2

The tangent function has an infinite number of poles. If you do not specify the interval, poles cannot find all of them. It issues a warning and returns an empty symbolic object.

syms x
poles(tan(x))
Warning: Unable to determine poles.
ans =
Empty sym: 0-by-1

If poles can prove that the input does not have poles in the interval, it returns empty without issuing a warning.

syms x
poles(tan(x), x, -1, 1)
ans =
Empty sym: 0-by-1

Return orders along with poles by using two output arguments. Restrict the search interval to (-pi, pi).

syms x
[Poles, Orders] = poles(tan(x)/(x-1)^3, x, -pi, pi)
Poles =
-pi/2
pi/2
1

Orders =
1
1
3

Return the residues and orders along with the poles by specifying three output arguments.

syms x a
[Poles, Orders, Residues] = poles(a/(x^2*(x-1)), x)
Poles =
1
0
Orders =
1
2
Residues =
a
-a

## Input Arguments

collapse all

Input, specified as a symbolic expression or function.

Independent variable, specified as a symbolic variable.

Search interval for poles, specified as a vector of two real numeric or symbolic numbers (including infinities).

## Tips

• If poles cannot find all nonremovable singularities and cannot prove that they do not exist, it issues a warning and returns an empty symbolic object.

• If poles can prove that the input does not have poles (in the specified interval or complex plane), it returns empty without issuing a warning.

• a and b must be real numbers or infinities. If you provide complex numbers, poles uses an empty interval and returns an empty symbolic object.

## Version History

Introduced in R2012b