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These are replies submitted by kiraMou

@Mariusz Iwaniuk 

for my point of view (numerically), It is better to keep  k(x) in the momentum space because you will need to deal with the convolution numerically, then you will have just to multiply both functions (k and log(1+f_1)) instead of dealing with convolution' integrals. 

@Mariusz Iwaniuk  it works, thank you !


Thank you very much  @vv  for your help. when I tried to run it, it gives me the following  error "Error, invalid sum/difference" . The cursor is pointing on 



Thank you @vv . Yes, Indeed. There are too many solutions and some of them are identical. I just learnt that the physical solutions are expected to sit on the two lines Im(x_j) ± Pi/2. Therefore, how to avoid physically meaningless solutions and identical solutions?

@Thomas Richard  it is done.

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