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Integration
2

Integration

Integration

(OP)
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
www.ozemail.com.au/~denniskb

RE: Integration

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

RE: Integration

(OP)
Thanks 3DDave.

Yes it is a sum and not an integration.

I am trying to use the online Wolfram calculator

Dennis Kirk Engineering
www.ozemail.com.au/~denniskb

RE: Integration

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:

https://www.wolframalpha.com/input/?i=infinite+ser...

It did not seem to have a way to solve for a particular summation.

RE: Integration

Try Sum[s^2/(n^2 - s^2), {n, 0, Infinity}]=0.48



RE: Integration

(OP)
petb entered and formula recognized but it does not solve for S which is the solution I need?

Dennis Kirk Engineering
www.ozemail.com.au/~denniskb

RE: Integration

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.

RE: Integration

Alternatively let Wolfram give you a couple of solutions like this: Link.

Hope this helps
/PB

RE: Integration

(OP)
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
www.ozemail.com.au/~denniskb

RE: Integration

try

CODE --> WA

solve (-1 - Pi s Cot[Pi s])/2 - 0.48=0 for s>0, s<1 

RE: Integration

(OP)
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
www.ozemail.com.au/~denniskb

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