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Plus distributions - general form #34

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alecandido opened this issue Apr 22, 2020 · 3 comments
Closed

Plus distributions - general form #34

alecandido opened this issue Apr 22, 2020 · 3 comments
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math formulas, theorems & co.

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@alecandido
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We are wondering if it is possible on general grounds to reorganize something of this kind:

r(z) + d \delta(z) + \sum_{k=0}^\infty c_k \left( \frac{\log^k(1-z)}{1-z} \right)_+

using constant coefficients for the distribution part:

\tilde{r}(z) + \tilde{d} \delta(z) + \sum_{k=0}^\infty \tilde{c}k \left( \frac{\log^k(1-z)}{1-z} \right)+

If this is possible:

  • we are thinking about rewriting our DistributionVec a little in order to collect all the singular bits in a single one (so we will have a fixed amount of components equal to 3 for all orders)
  • just do this we only need to:
    • include in coefficient functions definition the log(1-z) ** k / (1-z)
    • multiply in the convolution just for the pdf difference pdf(x/z)/z - pdf(x), that is available since what we currently are doing is multiplying each one of these two terms by a factor that is constant in the second expression (\tilde{c}_k)
@alecandido
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This is exactly what it is done by Vogt in his calculations (e.g.: c2_{ns}^{(3)})

@alecandido alecandido added the math formulas, theorems & co. label Apr 23, 2020
@felixhekhorn
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see #53

@alecandido alecandido linked a pull request Jul 28, 2020 that will close this issue
@felixhekhorn
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done in #72

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