How can I solve a sum of two variables function?

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

[Walter Roberson]

syms I U(t,M)
temp = symsum(1/(2*I-1)*exp(-(2*I-1)^2 * U), I, 1, inf)

temp(t, M) = 

int(temp, M, 0, inf)

ans(t) = 

However I am not sure what you mean by integral in dLnM -- you are integrating with respect to the log of M??

[3Nz0]

many thanks for your help.

Yes, I want integrate with respect to dlogM or dM/M.

[Walter Roberson]

Well the above shows integral with respect to M. You may have noticed that when U is an indefinite function that the result you get is not useful.

[3Nz0]

I have the expression of U(t, M). t and M are two vectors. I solved the problem discretizing the function, so U is a matrix. However I need to a function because 1)I want to estimate some parameters with fminsearch() 2)the result from integral with Simpson or traps method is a little bit higher then the desired results. Thank you, again

[Walter Roberson]

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.

Answer 1

[Swetha Polemoni]

Hi Enzo,

It is my understanding that you want to find intergation of series sum. You may these answers helpful

Integration of a Series Sum Follow

Integrating a multivariate function w.r.t. a single variable

Hope this helps