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.

Details

Examples

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Basic Examples  (3)

Use as an expansion point and direction:

Use as an integration limit:

Use as a limiting point:

Scope  (6)

Some directions have a special StandardForm:

Use inf 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:

Applications  (2)

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:

Introduced in 1988
 (1.0)