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Hey guys, I am learning real analysis right now, and I came across this assignment. I know you cant find a factorial of a negative number, but this confuses me, how does this work? Can someone please explain to me what is happening? How do you know that (-3/2 n) = (-3/2*(-5/2)*...*(-3/2-n+1))/n!
And how does that grow into a double factorial?
How do you even calculate a double factorial?
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>>177053
I don't know that you can do this with negative numbers, but isn't that the definition?
Source: Wikipedia https://en.wikipedia.org/wiki/Binomial_coefficient
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>>177053
Also double factorials are defined first thing on google http://mathworld.wolfram.com/DoubleFactorial.html In essence it's multiplying every other number. The reason it becomes that is because there is an n amount of 2s (2^n) which multiply each of the n numbers in the original factorial as shown in the 2^n * n! line.
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>>177053
>I know you cant find a factorial of a negative number
Of course you can, don't you know -½!=√π or sin(πx)/πx = 1/(x!)(-x!)
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