How can I solve a sum of two variables function?

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3Nz0
3Nz0 on 24 Feb 2021
Commented: Walter Roberson on 4 Mar 2021
Hello.
I have a two variables function: f=U(t,M).
I need to solve the integral (from 0 to +Inf) in dlnM of the following sum:
F(t,M) = sum(i odd) (1/i^2)*exp(-i^2 * U(t,M))
If anyone can help me, I will be appreciate it.
Thank you
  5 Comments
Walter Roberson
Walter Roberson on 4 Mar 2021
If M is a vector then you cannot integrate with respect to M.
At present, you have no hope of getting a closed form integral as long as you leave U as an indefinite function. If you put in the actual definition for U then you might get a useful result, perhaps. I was recently assisting someone with a broadly similar expression in which it turned out that what they were doing could be written in terms of JacobiTheta4.

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Answers (1)

Swetha Polemoni
Swetha Polemoni on 2 Mar 2021
Hi Enzo,
It is my understanding that you want to find intergation of series sum. You may these answers helpful
Hope this helps

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