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Jul 2, 2022 at 7:01 comment added BabaYaga I agree that your integral is divergent. This can be also seen by just expanding your result around a=0. My question: whether a series expansion is permissible on both sides. If yes, then it would be an infinite sum of finite terms/integrals. One of which would be the integrand in the question. In some way, the divergence will be regulated with 1/a kind of term.
Jul 2, 2022 at 6:47 comment added BabaYaga Btw I see that you have started with a different integration and then taking a->0.
Jul 2, 2022 at 6:31 comment added BabaYaga Then the question is after your comparison plot if one can compare coefficients of ‘a’ which is finite and corresponds to the original integral.
Jul 1, 2022 at 22:24 history answered Andreas CC BY-SA 4.0