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The gamma function is a fundamental example of an interesting function defined only on the integers which has an analytic (meromorphic) continuation to the whole complex plane. This ability to extend an interesting, seemingly discrete function to a complex differentiable function motivates a lot of later material.

Answered by Davidac897

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The gamma function is a fundamental example of an interesting function defined only on the integers which has an analytic (meromorphic) continuation to the whole complex plane. This ability to extend an interesting, seemingly discrete function to a complex differentiable function motivates a lot of later material.