# This is strange too

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?

matt grime
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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.

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

matt grime
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And integrating anything is ever fun?

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

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

Zurtex
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matt grime said:
Hmm, not my idea of fun, but then all of analysis that isn't trying to be algebra is dull.
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 :!!)

matt grime
Homework Helper
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.

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shmoe
Homework Helper
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.

BobG
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JonF said:
The integral of (fu)dn is, such that f and u are constants
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.

HallsofIvy
Homework Helper
matt grime said:
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.

Zurtex
Homework Helper
matt grime said:
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.
: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.

matt grime
Homework Helper
HallsofIvy said:

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

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

Zurtex
Homework Helper
abia ubong said:
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
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.

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.

matt grime