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comment Making mathematica do regulated integrals
SO taking the "limit" will not work? As in Mathematica knows how to take "limits" - right? So can't one use that inbuilt feature somehow?
1d
asked Making mathematica do regulated integrals
Apr
2
accepted How does Mathematica understand branchcuts of the complex logarithm?
Apr
1
comment How does Mathematica understand branchcuts of the complex logarithm?
If Mathematica is not choosing a contour then how is it computing the contour integral? Is there any valid meaning to this integral without a choice of branch avoiding contour and an associated limiting prescription? Thats is why I asked if Mathematica's answer is something meaningful? Because if it is not choosing a proper branch avoiding contour and a limiting process, it means it doesn't understand what a branch-cut is - right? Because technically one cannot just integrate across a branch-cut - right?
Mar
30
comment How does Mathematica understand branchcuts of the complex logarithm?
And how do I understand your $\sigma$ - what is the graphical/physical significance of that number? How do I see that physically/graphically? Is there a geometrical way to see this $\sigma$? Why did you think of it?
Mar
30
comment How does Mathematica understand branchcuts of the complex logarithm?
Thanks for the efforts! So if I let the branchcut be the default - as in upwards along the positive imaginary axis starting from point $ai$ then doing this contour integration on the UHP semicircle would have entailed taking a key-hole contour with the hole about the branchpoint and a semicircular bump about each pole on the positive imaginary axis on both sides of the key etc - so is Mathematica's answer when asked to integrate $f$ (your notation) along the semicircle the same? I mean when Mathematica is integrating $f$ is it taking into account the branch point at $ai$ and poles of Tanh?
Mar
29
comment How to find the x-axis intersections/zeroes of a parametrized integral?
@Kuba But is there a way to ask Mathematica is there is a singularity there? Like is there a way in which Mathematica can be asked to find out divergences in a function in a given interval?
Mar
28
comment How to find the x-axis intersections/zeroes of a parametrized integral?
@Kuba It removes the vertical line . But what does it really do mathematically?
Mar
28
comment How to find the x-axis intersections/zeroes of a parametrized integral?
@Kuba Thanks! So what do those vertical lines indicate? Can you kindly write the full command - as in where in the "Plot" function do I insert that?
Mar
27
asked How to find the x-axis intersections/zeroes of a parametrized integral?
Mar
26
awarded  Custodian
Mar
26
reviewed Approve suggested edit on How does Mathematica understand branchcuts of the complex logarithm? [Part 2]
Mar
26
asked How does Mathematica understand branchcuts of the complex logarithm? [Part 2]
Mar
26
comment How does Mathematica understand branchcuts of the complex logarithm?
In your last plot all the red lines are branch cuts -right? Then you have moved the branchcut along the x-axis? That will complicate matters - because I want to understand via complex analysis what is the behaviour of the integral of the function along the real line - thats the main objective...
Mar
26
comment How does Mathematica understand branchcuts of the complex logarithm?
Thanks or this amazing answer - I simply don't know so much Mathematica! Can you say if my conclusions were right that I got using Mathematica about the $A$ dependence and the vanishing of the integral about the branchpoint?
Mar
26
asked How does Mathematica understand branchcuts of the complex logarithm?
Mar
26
comment Asymptotic expansion
I mean - Tanh[x] goes to 1 as x goes to Infinity - then shouldn't Mathematica have substituted a 1?
Mar
26
comment Asymptotic expansion
More readably I want to expand asymptotically in $M$ for some given $x , a >0$ the function, $M^2 e^{2ix} Tanh[\pi M e^{ix}] Log[M^2 e^{2ix} + a^2]$
Mar
26
awarded  Benefactor
Mar
26
comment Asymptotic expansion
Here as earlier again the "Tanh" function doesn't get expanded - why?