# This is strange too

1. Apr 27, 2005

### abia ubong

hey i need help with this as a high school grad ,and one people think happens 2 be a maths prodigy a junior student came once and asked me 2 help him integrate x! i could not give a solution ,now pls can anyone help with this puzzle?

2. Apr 27, 2005

### matt grime

What makes you think x! is even a function of a real variable as opposed to one of integers? There is a function Gamma, that agrees with the factorial at the integers, why don't you look it up? The Gamma Function, see, eg, mathworld.

3. Apr 27, 2005

### JonF

Integrating the Gamma function isn’t going to be fun.

4. Apr 27, 2005

### matt grime

And integrating anything is ever fun?

5. Apr 27, 2005

### JonF

The integral of (fu)dn is, such that f and u are constants

6. Apr 27, 2005

### matt grime

Hmm, not my idea of fun, but then all of analysis that isn't trying to be algebra is dull.

7. Apr 27, 2005

### Zurtex

I love analysis, I used to love tricky integrals when I was first learning them as well

Give me any difficult maths challenge and I'll find some fun in it :!!)

8. Apr 27, 2005

### matt grime

Evidently you've never sat through a seminar on improving an upper bound from k^2 to k^{1.9999999999} on an eigenvalue of some operator defined on some probably oddly shaped domain, delivered in Russo-English for the benefit of the three other Russian analysts in the room with the poor sodding post grads (who were all algebraists/geometers, if they're different) like me who, at the time, didn't think they should miss these kinds of things.

Last edited: Apr 27, 2005
9. Apr 27, 2005

### shmoe

Even better when you consider the k^2 bound probably takes 15 lines or less to prove while the k^{1.9999999999} takes 15 pages. For 30 pages you can improve this to k^{1.9999999995}.

If something interesting happens at k^{3/2} the next 50 years will see hundreds of impenetrably dense technical pages that improve the bound to k^{1.893453} before someone with a new bright idea comes by and hammers out k^{3/2} on the back of a napkin.

10. Apr 27, 2005

### BobG

Not as fun as $$\frac{dx}{dn}=fu e^{-x}$$ such that f and u are constants. Although it seems more fun while you're doing it than when you're done.

11. Apr 27, 2005

### HallsofIvy

12. Apr 27, 2005

### Zurtex

:rofl:

Well, I assure you, I may not have had go through something quite so obscure but I've had my pains. I do remember sitting through 7 lectures on Euclid Algorithm, each one explaining no more than the last, in less than 2 weeks because the lecturers never bothered checking with each other what they were covering. I remember sitting through 5 lectures on the Taylor series without ever having ever come to a single example or how you generally derive them, after already previously encountering them thoroughly. The worst one at the moment is my "Advanced" Calculus lecture who knows clearly a lot less about the subject than I do and frequently makes mistakes that are on the level of a P.E high school teacher trying to teach it.

13. Apr 28, 2005

### matt grime

Oh, not really, I always think that of analysis; do I need a special reason?

14. Apr 28, 2005

### abia ubong

u all not helping i am a high school grad and u all talk of analysis related problems those are not helping ,c'mon u are here 2 help and be helped

15. Apr 28, 2005

### Zurtex

f(x)=x! is a function that goes from integers to integers. Generally for something to be integrated it needs to go from real numbers to real numbers, otherwise there is no area underneath it.

16. Apr 28, 2005

### abia ubong

but i have been working on it thugh havenot gotten good result i was tryiong 2 find the general expansio of the factorial mean,but have not gotten it yuet if u can help give a general formula on how 2 expand generally ,i could get it.

17. Apr 28, 2005

### matt grime

For the third time, it makes no sense to talk of integrating x! at the level you're at. It is not a function from the Real line to the Real line. We told you that you need to give a function from R to R, which an be done, (in several, nay, infinitely many ways) that agrees with the factorial at the integers. So, you see, the question does not a priori make sense.