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be all such that with . The fundamental strip of is defined to be the largest open strip on which it is defined. For example, for the fundamental strip of

is . As seen by this example, the asymptotics of the function as define the left endpoint of its fundamental strip, and the asymptotics of the function as define its right endpoint. To summarize using Big O notation, if is as and as , then is defined in the strip .

An application of this can be seen in the gamma function,

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