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Built-in Mathematica Symbol

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.

Use as an expansion point and direction:

Use as an integration limit:

Use as a limiting point: