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- What does the factorial of a negative number signify?
So, basically, factorial gives us the arrangements Now, the question is why do we need to know the factorial of a negative number?, let's say -5 How can we imagine that there are -5 seats, and we need to arrange it? Something, which doesn't exist shouldn't have an arrangement right? Can someone please throw some light on it?
- complex analysis - Why is $i! = 0. 498015668 - 0. 154949828i . . .
Why is this? I know what a factorial is, so what does it actually mean to take the factorial of a complex number? Also, are those parts of the complex answer rational or irrational? Do complex factorials give rise to any interesting geometric shapes curves on the complex plane?
- factorial - Why does 0! = 1? - Mathematics Stack Exchange
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 $0 <k < n$ A reason that we do define $0!$ to be $1$ is so that we can cover those edge cases with the same formula, instead of having to treat them separately We treat binomial coefficients like $\binom {5} {6}$ separately already; the theorem assumes
- Factorial, but with addition - Mathematics Stack Exchange
106 This question already has answers here: What is the term for a factorial type operation, but with summation instead of products? (4 answers)
- Defining the factorial of a real number - Mathematics Stack Exchange
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
- Observation of Linking Factorial, Carmichael of the Factorial, and the . . .
My guess of why this totient-bypass relationship exists by virtue of factorial(n) having comprehensive coverage of everything up to n, thus totient of individual prime factors would never contain more copies of it than the largest power of each prime, so the LCM of them HAS to be a subset of the factorial itself
- How do we calculate factorials for numbers with decimal places?
I was playing with my calculator when I tried $1 5!$ It came out to be $1 32934038817$ Now my question is that isn't factorial for natural numbers only? Like $2!$ is $2\\times1$, but how do we e
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