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# 14: Analytic Continuation and the Gamma Function

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In this topic we will look at the Gamma function. This is an important and fascinating function that generalizes factorials from integers to all complex numbers. We look at a few of its many interesting properties. In particular, we will look at its connection to the Laplace transform. We will start by discussing the notion of analytic continuation. We will see that we have, in fact, been using this already without any comment. This was a little sloppy mathematically speaking and we will make it more precise here.

Thumbnail: Analytic continuation from $$U$$ (centered at 1) to $$V$$ (centered at a=(3+i)/2). (CC BY-SA 4.0 International; Ncsinger via Wikipedia)

14: Analytic Continuation and the Gamma Function is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Jeremy Orloff via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.