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 Oct 10 comment A 1D numerical integral Mathematica cannot compute, from physics Usually for what I need $h (\omega)$ is the result of a numeric integral over other variables, so does not have an analytic form. The problem is more complicated (two numeric integrations + an infinite sum to end with...). Modifying the contour choice is great advice, thanks! I'm looking into it right now... Oct 10 comment A 1D numerical integral Mathematica cannot compute, from physics J.M. is back: care to elaborate? The usual way in physics textbook to calculate that sum is to convert it to a contour integral. I'm no expert in this field, which other options do I have to numerically calculate an infinite sum? Note that here I chose a very simple $h(\omega)$ usually it is more complicated... Oct 10 comment A 1D numerical integral Mathematica cannot compute, from physics Many thanks! I modified the question to add it! Oct 10 revised A 1D numerical integral Mathematica cannot compute, from physics added 43 characters in body Oct 10 comment A 1D numerical integral Mathematica cannot compute, from physics I just tried $\beta=10$ and $\beta=20$, the convergence problems are unchanged. They disappear in the low-temperature limit, $\beta=100$, for example. Oct 10 comment A 1D numerical integral Mathematica cannot compute, from physics Sorry, I forgot to mention it, for the plots I am using $\beta=0.2$. Physically speaking it is the inverse temperature, so $\beta=0.2$ corresponds to high temperatures. Oct 10 asked A 1D numerical integral Mathematica cannot compute, from physics Aug 14 awarded Nice Question Jun 1 awarded Popular Question Nov 27 awarded Notable Question Jul 2 awarded Curious May 14 comment Converting HeavisideTheta[]s and Sign[]s functions to a single Piecewise[] Done. Actually it's not a quartic strictly speaking, but while solving the equation in order to find the zeroes, you get a quartic and so you get 4 solutions in the end. May 14 revised Converting HeavisideTheta[]s and Sign[]s functions to a single Piecewise[] added 140 characters in body May 14 comment Converting HeavisideTheta[]s and Sign[]s functions to a single Piecewise[] No, they are not. Some of them are quartic, however it's possibile to find the zeroes of each one analytically. May 14 asked Converting HeavisideTheta[]s and Sign[]s functions to a single Piecewise[] May 14 awarded Commentator May 14 comment Is Mathematica really getting this limit wrong? Thank you very much Daniel. Just one additional question: why is everyone saying that the limit should go unevaluated? Isn't Sign[A] a correct result? May 13 accepted Is Mathematica really getting this limit wrong? May 13 asked Is Mathematica really getting this limit wrong? Mar 1 comment Non-linear integral equation @george2079: it should converge, at least it is eq. 5 in this paper: journals.aps.org/prl/pdf/10.1103/PhysRevLett.74.1633 The authors refer to an unpublished paper for the numerical part, commenting as follows: letting $x=\tan(\beta)$, we set up a Gaussian-quadrature grid for $\beta$ and convert the above equations into a matrix form which can be solved iteratively. The logarithmic singularities are treated separately.