Use as an expansion point and direction:

Use as an integration limit:

Use as a limiting point:

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:

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 the Wolfram Language assume symbols to represent numbers: