| I understand! Thank you for the explanation. I have also now noticed that users.pdf contains a caveat about intnum. It would be good if it were possible for the algorithm to see that such a problem might occur and then automatically switch to Simpson approximation - but perhaps this is too complicated. Regards, Damian Rössler
Dear Bill, thank you for this. What do you mean by « an asymptotic singularity at I »?
The integral is along the real line, so it never meets any singularity of the function (in particular, log(x+I) is always well-defined). The efficiency of the Double-Exponential method comes from strong assumptions on the regularity of the function near its integration path (or equivalently, the decay of its Fourier transform in terms of which we can express the integration error). This example is typical of a pole which is relatively close to the integration path (relative to the path length), resulting in a very slow convergence of the method (this can be improved by splitting the integration path, as Bill suggested, or by taking into account an extra series coming from the pole).
Pascal Molin (who spent some time studying those phenomena :-)
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