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Integration 2

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denniskb

denniskb

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How do I enter the following into an integration calculator to solve for s?
Sum(n= 0 to infinity, s^2/(n^2-s^2)) when the sum value has a known value (i.e. sum() = 0.40348)

Dennis Kirk Engineering
 
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Which integration calculator? Summation isn't integration, so that puzzles me. It's summation of an infinite series.

 
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I entered it as a series on Excel and totaled up the first hundred terms. Because of the n^2 in the denominator it acts like it converges really fast, though with infinity, maybe it adds up.

I tried at Wolfram:


It did not seem to have a way to solve for a particular summation.
 
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Try Sum[s^2/(n^2 - s^2), {n, 0, Infinity}]=0.48



 
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You get the answer in this form:
1/2 (-π s cot(π s) - 1) = 0.48

Rewrite as below and put it back in WA:
(-1 - Pi s Cot[Pi s])/2 - 0.48=0

This will have multiple solutions.
 
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Alternatively let Wolfram give you a couple of solutions like this: Link.

Hope this helps
/PB
 
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Thanks petb
Re-entering the original formula in the form suggested by WA provides several solutions one of which is the one I want (i.e. 0 < s < 1)
Is there a way to limit the range for s within the WA input?

Dennis Kirk Engineering
 
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try
Code: 
solve (-1 - Pi s Cot[Pi s])/2 - 0.48=0 for s>0, s<1

 
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Or in Excel:

Solver_ex_cjy07s.png


Doug Jenkins
Interactive Design Services
 
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Agent666 much appreciated as this cleans up the WA output nicely

IDS yes this is also useful though WA provides the same on the second pass

Can anyone suggest a way to solve directly from the original formula in Excel via macro?

i.e. Sum[s^2/(n^2 - s^2), {n, 1, Infinity}]=0.40435 for s>0, s<1

Note that I need to run this calculation multiple times for various values of = 0.40438 and thne again with a slightly different formula and then run this for various values of the function.

i.e. Sum[s/(n^2 - s^2), {n, 1, Infinity}]=0.56037 for s>0, s<1

Dennis Kirk Engineering
 
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petb and IDS already showed how that could be done

If
Sum[s^2/(n^2 - s^2), {n, 0, Infinity}] = C​

Then
(-1 - Pi s Cot[Pi s])/2 = C​

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! faq731-376 forum1529 Entire Forum list
 
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