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- Factorial, but with addition - Mathematics Stack Exchange
Is there a notation for addition form of factorial? $$5! = 5\times4\times3\times2\times1$$ That's pretty obvious But I'm wondering what I'd need to use to describe $$5+4+3+2+1$$ like the factorial $5!$ way EDIT: I know about the formula I want to know if there's a short notation
- factorial - Why does 0! = 1? - Mathematics Stack Exchange
$\begingroup$ The theorem that $\binom{n}{k} = \frac{n!}{k!(n-k)!}$ already assumes $0!$ is defined to be $1$ $ Otherwise this would be restricted to $0 <k
- What does the factorial of a negative number signify?
For example: the factorial of zero i e an empty set ( doesn't occur) is 1 As the empty set can be arranged only in 1 way - i e by filling nothing Now, let's take an example: 5 distinct seats How many ways 5 distinct seats can be arranged? - 5! ways i e 120 So, basically, factorial gives us the arrangements
- Defining the factorial of a real number - Mathematics Stack Exchange
$\begingroup$ Some theorems that suggest that the Gamma Function is the "right" extension of the factorial to the complex plane are the Bohr–Mollerup theorem and the Wielandt theorem $\endgroup$ – kuzzooroo
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