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For example,$N!$和$\Gamma(z)$ are discrete formula and it's continuous counterpart .Maybe,the word continuous is not appropriate here

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I think this question should be slightly reworded, e.g., as a request for examples of fruitful interpolation. One family of examples that comes to mind are zeta functions and L-functions ($p$-adic or complex) as interpolations of sequences of periods. – S. Carnahan♦ May 3 2011 at 15:35
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 "Most interesting" is quite subjective. Like many (most?) mathematicians, I enjoy the interplay between the continuous and discrete, so I want to like this question, but I think it could use some firming up. – Pete L. Clark May 3 2011 at 15:35
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 And while you are at it, what is your favorite number? – Igor Rivin May 3 2011 at 16:17
With the edit, it's not clear what the point of the question is. – Ryan Budney May 3 2011 at 18:11
@Ryan,I have shown an example,and I thank there are a lot of such pairs ,but no one has shown both of them or has found the corresponding counterpart,which may lead to interesting discovery. – XL May 3 2011 at 20:28
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closed as not a real question by Igor Rivin, Ryan Budney, Zev Chonoles, Scott Morrison♦ May 3 2011 at 20:57

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