Using an alternate definition for the exponential function leads to the same result when expanded as a Taylor series.

An alternate definition often used by biologists is any species, not just plants, that can quickly adapt to any environment.

This is an alternate definition of the polylogarithm function.

This alternate definition gives exactly the same classifications as the first definition.

An alternate definition of process migration is used in integrated circuit design and engineering.

No commenter proposed an alternate definition of "edited for Internet distribution."

When not listing river lengths, however, alternate definitions may be used.

In recent years, an alternate definition for the perfect magic cube has gradually come into use.

From such ideas came the alternate definition of "dinosaur" as something out of date.

He promotes an alternate definition of magic as "doing the impossible".