Can we have negative factorial?
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We will figure out if we can do the factorial of -1/2 and the factorial of -1. We will be using the extension of factorial via the Pi function and the Gamma function. I will also give a summary at the end on when we can have negative factorials.
Pi & Gamma functions: • extending the factoria...
0^0 convention: • 0^0=1 is "seriesly" us... ,
negative factorial, • Can we have negative f...
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@heliocentric1756 6 жыл бұрын
10:50
@Jacob-uy8ox 6 жыл бұрын
try to do a complex factorial
@ramez2775 6 жыл бұрын
"How many ways can you arrange negative 1 apples?"
@ScottMaday 5 жыл бұрын
someone:
@MichaelGrantPhD 2 жыл бұрын
As I said in your poll, this is a definition issue. There are of course well defined ways to extend the factorial function beyond the nonnegative integers. But the exclamation mark is reserved for that original, integral definition. It's unfortunate that the Gamma function is "off by one" or it would be easy to just use that and call it a day.
@sdsa007 2 жыл бұрын
Thank you! This is very advanced for me , but I am so glad I can find answers to my math questions! Awesome!
@factsheet4930 6 жыл бұрын
Great this reminded me of the old questions we got back in elementary school where they asked things like:
@themsk9923 2 жыл бұрын
You are literally bringing those questions which i always thought about 👍 thanks 😊
@michaelspence2508 5 жыл бұрын
You could also look at (-1)! as a sequence. Every time you subtract 1 you multiply by a larger value (in terms of absolute value) and change the sign. Roughly speaking it looks (vaguely) like the graph of x*sin(x) in that it approaches both infinity AND negative infinity which is why saying (-1)! = infinity is incorrect.
@donotlaughagain5093 6 жыл бұрын
factOREO!
@ebz4125 6 жыл бұрын
Was wondering if you can make a video on the analytical continuation / poles of the gamma function? That'd be interesting.
@tomatrix7525 3 жыл бұрын
Extremely nice vid bprp
@jorgeeduardopereztasso6134 6 жыл бұрын
I remember that in my Calculus exam my teacher put a question with that divergent integral... It took me like all the exam time to realize that cannot be solved. XD
@trueriver1950 6 жыл бұрын
I prefer the second method, from
@joaomarcosdossantos7593 6 жыл бұрын
Hi, I really enjoy your videos. Could you show something about the wau(or digamn) number. I saw it, and got curious. Thanks for your amazing videos here.
@atrumluminarium 6 жыл бұрын
If I remember correctly, there's a neat trick where you can "extract" the divergences/poles (on the negative integers) by using the by-parts expansion of Γ. This gives
@General12th 6 жыл бұрын
Yay! This makes so much sense!
@Filip6754 6 жыл бұрын
But can you do dis?
@giladu.6551 6 жыл бұрын
Keep doing what you're doing!
@Mephisto707 6 жыл бұрын
Can you show us the graph of the Pi function?