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A compact formula of DnPtf(x) and the estimation of ∥DnPtf(x)∥HS are also given.
Using the theory of Jordan chain, a compact formula of Parisian ruin probability is given.
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Using the scale function, Loeffen et al. [11] gave a compact formula for the Parisian ruin probability of a spectrally negative Lévy risk process.
Now we derive a compact formula for (g_{S}left( lambda right) ) to show a type of calculation that is regularly needed for nonconstant canonical spectral densities.
We thereby obtain a compact formula for the WKB expansion.
These findings yield a compact formula for cumulants on a fixed Wiener chaos, virtually replacing the usual "graph/diagram computations" adopted in most of the probabilistic literature.
What I like about this paper is that in one line of algebra we derived a compact formula that accounts for 50 years of experiments.
Compact formulas of βk for WENO schemes are also presented.
A new and compact formula for the base transit time in an npn bipolar junction transistor is derived.
A compact analytical formula for the nonlinear coefficient of the absorber is then derived.
Using the geometrical interpretation of least squares is the fastest manner to demonstrate this formula and leads to the most compact formula.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com