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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
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Nov
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Jul
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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.