Tricky Problems (***)

Simplify the equation to its simplest form;





where is Riemann's zeta function, is the gamma function, is the del operator, denotes the inverse Laplace transform, is the nth Chebyshev polynomial of the first kind, is a simple closed curve bounding a region having as an interior point, is a simplex of an oriented simplicial complex and [σ^m, σ^(m - 1)] is an incidence number, is a compact, orientable, differentiable k-dimensional manifold with boundary in and is a -form in , defined, and at all points of , and is Dirichlet's eta function.

EDIT: The last bit of that equation is cut off (the integral involving Dirichlet's Eta function). To see it, go here; http://www.physicsforums.com/latex_images/25/2504352-2.png

Easy. The answer is 2

problem with your image code there

Damn... the trouble with posting an image link to a LaTeX code that's been rendered is that sometimes they may contain the ] and [ brackets, which, if removed, can be crucial to the LaTeX coding. Going to have to find a way around it...

Okay, fixed. I uploaded the image somewhere else.

For those who don't have that much time on their hands, here is an easier challenge (but still feels nice completing it);

Simplify the equation to its lowest form;



where p is prime.

^^ Fail?

Did you have a go at the bottom problem? I think GCSE students should be able to manage it... a lot of the stuff can be cancelled out from first glance, but it should be a nice test going through it.

i don't think that website likes hotlinking o_O

i keep seeing physicsforum.com

Are you sure? It looks fine to me... I edited the changes into the first post.

can I show my workings out?

EDIT: Problem Fixed, nothing to see here

That is rather strange... I see the images fine.

You can see the images here in their respective order;

http://www.physicsforums.com/latex_images/25/2504352-1.png
http://www.physicsforums.com/latex_images/25/2504352-2.png

or the same image but that's just as good.

We love you Ric =D wrote:or the same image but that's just as good.

? They're different images...

maybe when ever I see a complex question I always cover it up with www.physicsforums.com

I'll upload it on to imageshack... I hope their compression doesn't suck, though.

What about the easier challenge? Is it visible?

yes tis
oooh modish

Okay, it should be fixed now.

Enjoy.

OK carry the one, finished I'll wait for everyone else before I ruin it for them

'Carrying the one' is actually a step in the process to determine a solution for the easier challenge. O_o

now I'm confused I thought I was dividing shit in the first one you don't wanna know how wrong I was.

There is a lot of dividing in the first one... you will notice how easily some of the things cancel out.

Hint: The divergence of a curl is zero.

i'm guessing you teach further maths cause no way have i heard anything about this on the syllabus in single

Well, the trickier challenge is mainly orientated towards those who have studied mathematics up to degree level, but some things you will have come across before - there is a surface integral in there, which is in the syllabus, and the gamma function is right at the start, which is essential in combinatorics.

Has anyone tried the easier challenge? Looking to see how the denominator is tackled on the LHS. Hint: Do we need to bother integrating e^(x^2)?

there's a lot of greek in this "maths" shiz they should try updating them equation's and what not instead of zeta our homme's should be puttin fallout 3 up in there faces know what I'm sayin