represents an infinite numerical quantity whose direction in the complex plane is unknown.
represents an infinite numerical quantity that is a positive real multiple of the complex number z.
- You can think of DirectedInfinity[z] as representing a point in the complex plane reached by starting at the origin and going an infinite distance in the direction of the point z.
- The following conversions are made:
Infinity DirectedInfinity -Infinity DirectedInfinity[-1] ComplexInfinity DirectedInfinity
- Certain arithmetic operations are performed on DirectedInfinity quantities.
- In OutputForm, DirectedInfinity[z] is printed in terms of Infinity, and DirectedInfinity is printed as ComplexInfinity.
Examplesopen allclose all
Basic Examples (3)
Some directions have a special StandardForm:
Use Infinity as an alternative input form:
Multiplying by a number changes the direction:
Unspecified or Indeterminate direction represents ComplexInfinity:
Finite or symbolic quantities are absorbed:
Extended arithmetic with infinite quantities:
In this case the result depends on the directions x and y:
Operations that cannot be unambiguously defined produce Indeterminate:
In this case the result depends on the growth rates of the numerator and denominator:
Use in mathematical functions:
Integrate along a line from the origin with direction :
Asymptotics of the LogGamma function at DirectedInfinity[z]:
Plot asymptotic value compared to function value in different directions:
Properties & Relations (3)
Simplify and FullSimplify can generate infinities:
A nested DirectedInfinity reduces to one DirectedInfinity:
DirectedInfinity is not a number:
Possible Issues (3)
Symbolic quantities might get lost in operations:
The Accuracy and Precision for DirectedInfinity refer to the direction argument:
Simplifications performed by the Wolfram Language assume symbols to represent numbers:
Wolfram Research (1988), DirectedInfinity, Wolfram Language function, https://reference.wolfram.com/language/ref/DirectedInfinity.html.
Wolfram Language. 1988. "DirectedInfinity." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/DirectedInfinity.html.
Wolfram Language. (1988). DirectedInfinity. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DirectedInfinity.html