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#1 2010-01-24 01:41:04

zetafunc.
Guest

how to simplify this equation?

ok, this is a very big help, but how do i simplify this?



where ζ is Riemann's zeta function, Γ(x) is the gamma function, ∇ is the del operator, L[sup]-1[/sup] denotes the inverse Laplace transform, T[sub]n[/sub] is the nth Chebyshev polynomial of the first kind, C is a simple closed curve bounding a region having z = a as an interior point, σ[sub]0[/sub][sup]m[/sup] is a simplex of an oriented simplicial complex and [σ[sup]m[/sup], σ[sup]m - 1[/sup]] is an incidence number, S is a compact, orientable, differentiable k-dimensional manifold with boundary in E[sup]n[/sup] and ω is a (k - 1)-form in E[sup]n[/sup], defined, and C[sup]1[/sup] at all points of S, and η(x) is Dirichlet's eta function.

can someone help me out? i have many questions to ask... i will ask them in the next posts, thx. ^^

#2 2010-01-24 05:17:02

Devantè
Real Member
Registered: 2006-07-14
Posts: 6,400

Re: how to simplify this equation?

The LHS of the equation reduces to y after noting that the divergence of a curl is zero, and

the

is cancelled by the integral in the denominator using the above form and a change of variables.

The right hand side presumably falls to a similar sort of identity application; I would guess the last two terms are zero and the first two fractions probably almost entirely cancel. Anywho, I'll let the interested figure the rest of it out. This will take a fair bit of time to do.

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#3 2010-01-24 06:10:21

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: how to simplify this equation?

Sheesh... now I understand all your posts.  I was wondering what it was you were trying to learn. lol

How much math have you had zeta?


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#4 2010-01-24 06:40:27

zetafunc.
Guest

Re: how to simplify this equation?

Hi Ricky, I am currently in year 10 and just started my GCSEs. However, GCSE maths is a cakewalk for me.....so I learn other things. My school don`t let me take a-level maths early, so I have to try and learn all of this on my own.....I cant afford a tutor or anything like that. all I have is a computer and a library i can go to (which drags).

i can differentiate + integrate functions and i know lots of little bits about many different things across maths... i try to learn as much as i can. Mr. Ricky, I read your set theory and group theory pages on mathsisfun, they are very good, but i am having trouble knowing where to go from there. sad

my current situation in maths is hard to explain, but i have knowledge of a lot of things, just not in great detail. i know quite a bit about calculus (well, up to a-level that is, i dont claim to be a calculus genius).

so i am basically wanting to ask questions that i don't know the answer to. thanks for your time. smile

#5 2010-01-24 07:56:03

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: how to simplify this equation?

i can differentiate + integrate functions

I'm guess that you learned this on your own?  Did you use a book, or just various web pages?  If you used a book, which?

The identities above involve:

Differential geometry
Analysis
Complex analysis
Vector calculus

Each of these merits their own study for at least a semester if not more.  In turn, to study these subjects, you should know "advanced calculus" (intro to analysis), abstract algebra, and differential equations.  So if you want to understand the identities involved above, this is fine.  But if you want to learn mathematics, then I recommend starting with a good solid foundation in calculus.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#6 2010-01-24 08:17:33

zetafunc.
Guest

Re: how to simplify this equation?

hi Ricky, I dont have any maths books. But, I learned from this website: http://edugratis.com/

I've done differential equations yeah.....but not analysis or abstract algebra. i googled "introduction to analysis" and it came up with this: Google Ebooks Introduction to Analysis

I am very eager to learn, and I will read this book. it is very difficult to learn all of this on my own....is very easy to forget things (because not an actual lesson with teacher to explain everything.....) and i probably miss out a lot of things (like statistics, I dont know that much about that, only basics (nCr, nPr, factorial, superfactorial, hyperfactorial, fibonacci, etc). if you could point me in the right direction from here, that would be good (i have just turned 15, i can go and try to find a maths book or if not an ebook somewhere, or i will go away and research). thank you for your time. smile

do you think its a wise move to google ebooks and read them off internet? i would print it out but thats a lot of pages (200) but i can read it bit by bit.

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