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DirectedInfinity

DirectedInfinity
represents an infinite numerical quantity whose direction in the complex plane is unknown.
DirectedInfinity[z]
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:
Use as an expansion point and direction:
Use as an integration limit:
Use as a limiting point:
Use as an expansion point and direction:
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Use as an integration limit:
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Click for copyable input
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Use as a limiting point:
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Some directions have a special StandardForm:
Use Esc inf Esc to enter :
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:
The value in different directions may vary:
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:
Simplify and FullSimplify can generate infinities:
A nested DirectedInfinity reduces to one DirectedInfinity:
DirectedInfinity is not a number:
Symbolic quantities might get lost in operations:
The Accuracy and Precision for DirectedInfinity refer to the direction argument:
Simplifications performed by Mathematica assume symbols to represent numbers:
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