The factorial of a positive integer [math]n[/math], denoted [math]n![/math], is the product of the numbers from [math]1[/math] through [math]n[/math]. It is also, happily, the result of a certain definite integral:
[math]\displaystyle n! = \int_0^\infty e^{-t}t^n\,dt[/math]
That definite i...
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