How to treat negative integer factorial function?

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dongsh2
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Dear all,

How to deal with negative integer factorial functions? I mean what expression formula can be substituted for this?
 

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I don't believe there is one. The Gamma function is the analytic continuation, but it has poles at the negative integers.
 
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The first thing you would have to do is define this "negative factorial function". Where did you find a reference to a "negative factorial function"? If this was given in some text exercise how was the negative factorial function defined?