Good luck!
Does anybody know the derivative of x!?
Prove it!
Does anybody know the derivative of x!?
Prove it!
How does that connect to "!"?shmoe said:The Gamma function has been beaten severely to death by mathematicians over the years. It turns up all over the place, so it was pretty naturaly for it to be studied extensively. It's a pretty basic function actually, similar to the trig ones. In fact:
G(x-1)G(x)=Pi/sin(Pi*x)
*stares at equation...................*This might seem like a mind-bending equation, but if you've studied some complex analysis and you think about the poles the functions on both side of the equation have, it's less mysterious.
Yes, that's why I asked it. Partial differentiation! Yuhoooo!!!nCr and nPr are defined in terms of factorials, so you could just think of them as products and quotients of Gamma. One thing to keep in mind though, is you have two variables n and r, so things get more complicated unless you restrict one of them to be a constant.
TruthSeeker said:How does that connect to "!"?
That's really bizarre, cause all values of sine are between -1 and 1... :/shmoe said:Gamma is quite obviously related to factorial. Gamma is related to sine by that formula. So your friendly neighbourhood factorial is some related to sine. It doesn't seem like there should be any connection between Gamma (which remember, is an extention of factorial) and trig functions, but it's actually quite natural.
Why? I tried to do that in my calculator, but I don't have an "i" button....Fraggle Rocker said:One key to this will be for you to figure out what the value of e^iPi is.
It's one of my best...It's a shame that trig was my worst math subject. It seems to be involved with almost every aspect of the universe.
TruthSeeker said:That's all cool, but why do we have to wait until the 2nd or 3rd year of university to learn that!? It's kinda dumb. This semester, I'm taking "Finite Mathematics" and I'm learning that Venn diagram stuff and probability stuff all over again. It is at least the fith time I've learnt that!!! Like... gimme a break! Why do I have to see that once again. It makes me sick, really. I wish I didn't need to waste my time with that anymore. The worse is that I don't feel motivated to study it again, so my marks just drop... :/
TruthSeeker said:That's really bizarre, cause all values of sine are between -1 and 1... :/
Well, ok... maybe I'm thinking about the y axis... But it is still weird..
Have you ever studied economics? In economics, there's something called marginal utility, which is the amount of satisfaction that a customer gets from a product after using it (or buying it) once again. This marginal utility drops as the quantity increases, because after consuming too much of one thing, you simply get tired of it. The same thing applies for Math. I've done it so many times that it became completely repetitive and useless for me. With less motivation to do the stuff, my marks finish dropping.shmoe said:If it's your 5th or 6th time taking it, I have to wonder how your marks are dropping. Shouldn't it be routine by now?
Isn't it hard to study on my own? How can I do it?It does look pretty strange. One thing to keep in mind is in the equation I gave relating Gamma to sine, the sine function was in the denominator, so the right hand side wanders off to infinity near the zeros of sine. The relations between all these functions, trig functions, hyperbolic trig functions, Gamma, e<sup>x</sup>, etc. will make more sense once you've studied some complex analysis (which you can do on your own).
TruthSeeker said:Isn't it hard to study on my own? How can I do it?