Riemann Sum (I think): lim[n->infty]sum[i=0,n][d/((d^2-{ir/n}^2)^{3/2})

[ColinConnelly]

I am struggling to solve this. I know it converges. I have approximated it with a large number of iterations in a spreadsheet - setting n at 10,000. But I can't seem to figure out the actual formula.

But, I don't even know if I have described the equation properly.

. . . . .\(\displaystyle \displaystyle \lim_{n \rightarrow \infty}\, \sum_{i=0}^n\, \dfrac{d}{\left(d^2\, -\, \left(\dfrac{ir}{n}\right)^2\right)^{3/2}}\)

Any help appreciated,

Thanks,
Colin.

 

[Dr.Peterson]

I am struggling to solve this. I know it converges. I have approximated it with a large number of iterations in a spreadsheet - setting n at 10,000. But I can't seem to figure out the actual formula.

But, I don't even know if I have described the equation properly.

. . . . .\(\displaystyle \displaystyle \lim_{n \rightarrow \infty}\, \sum_{i=0}^n\, \dfrac{d}{\left(d^2\, -\, \left(\dfrac{ir}{n}\right)^2\right)^{3/2}}\)

Any help appreciated,

Thanks,
Colin.

Can you tell us more about this? It does look a lot like a Riemann sum (with x = ir/n), but I don't see anything corresponding to dx = r/n. I may just be missing something, but I'd like to be sure you copied it correctly. Was it a problem you were given, or did you create it in some way yourself? What is the context?

 

[ColinConnelly]

G'Day Dr. Peter.

Not copied. This is actually a personal quest going over the past 17 years. I'm working on a protein folding algorithm. I am a programmer by trade and this equation will help determine the force field for molecules in my algorithm.

What I am trying to do is take this equation;

d/((d^2 - r^2)^(3/2)) and sum n times for each of one nth of r.

Cheers,

Colin.

 

[ColinConnelly]

Can you tell us more about this? It does look a lot like a Riemann sum (with x = ir/n), but I don't see anything corresponding to dx = r/n. I may just be missing something, but I'd like to be sure you copied it correctly. Was it a problem you were given, or did you create it in some way yourself? What is the context?

Hi,

This is a personal quest going back 17 years to solve a protein folding algorithm bottleneck.

I'm basically trying to get the sum of;

d / ((d^2-r^2)^(3/2))

for n iterations of one nth of r.

Cheers,

Colin.