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Yeah, I think Mathematica has some problems with the integration of Bessel functions. I am trying to somehow avoid the evaluation of the integral in the Cauchy principal value sense by removing the constant and thus making the integral weakly...
Thanks Hans, that gave me a very high value like -3521, I think that might not be the answer. I have a fortran code that uses the singularity subtraction to calculate and it gives a value of like 0.1000 for the integral from -1 to 1, I wanted to know...