Contact US

Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Students Click Here




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

RE: Integration

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

RE: Integration

Thanks 3DDave.

Yes it is a sum and not an integration.

I am trying to use the online Wolfram calculator

Dennis Kirk Engineering

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:


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

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

Dennis Kirk Engineering

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

RE: Integration

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

RE: Integration



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

RE: Integration

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

Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members! Already a Member? Login


Low-Volume Rapid Injection Molding With 3D Printed Molds
Learn methods and guidelines for using stereolithography (SLA) 3D printed molds in the injection molding process to lower costs and lead time. Discover how this hybrid manufacturing process enables on-demand mold fabrication to quickly produce small batches of thermoplastic parts. Download Now
Design for Additive Manufacturing (DfAM)
Examine how the principles of DfAM upend many of the long-standing rules around manufacturability - allowing engineers and designers to place a part’s function at the center of their design considerations. Download Now
Taking Control of Engineering Documents
This ebook covers tips for creating and managing workflows, security best practices and protection of intellectual property, Cloud vs. on-premise software solutions, CAD file management, compliance, and more. Download Now

Close Box

Join Eng-Tips® Today!

Join your peers on the Internet's largest technical engineering professional community.
It's easy to join and it's free.

Here's Why Members Love Eng-Tips Forums:

Register now while it's still free!

Already a member? Close this window and log in.

Join Us             Close