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So upon thinking about this more and playing with different assumptions when trying to integrate the above function(s), what I found was the following - $\int_{a}^{\infty} dt \frac{e^{i k t}}{t + i \tau} = e^{k\tau}\,\Gamma\left(k(-ia + \tau) \right)$, where $\Gamma$ is the incomplete Gamma function. Now, suppose I try doing this integral with ...


This is due to the sum of two very large numbers (coming from CosIntegral and SinhIntegral) being carried out without sufficient machine precision used to represent them. You can fix it giving an appropriate value of WorkingPrecision as an option to plot. You can see quite clearly that the problem comes from this by plotting the two functions (the one ...

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