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poles

Poles of expression or function

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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 offwith respect to variablevar.

example

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

example

[P,N] = poles(___)returns the poles offand their orders inN.

example

[P,N,R] = poles(___)returns the poles off, their orders, and residues inR.

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,polesuses the default variable determined bysymvar.

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

Find the poles with respect toaby 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,polescannot 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

Ifpolescan 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

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

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

  • aandbmust be real numbers or infinities. If you provide complex numbers,polesuses an empty interval and returns an empty symbolic object.

版本历史

Introduced in R2012b

See Also

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