# poles

Poles of expression or function

## Syntax

``P = poles(f,var)``
``P = poles(f,var,a,b)``
``````[P,N] = poles(___)``````
``[P,N,R] = poles(___)``

## 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

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```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

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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.