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Discover LudwigThe phrase 'by equation' is correct and usable in written English.
You can use it when referring to a mathematical or scientific equation that explains a certain phenomenon or process. For example, "The behavior of the particles can be described by equation 5.2."
Exact(56)
Consider again the binomial distribution given by equation (3).
The current in the circuit is given by equation (24).
The probability that the particular event occurs exactly i times is given by equation (3).
In infinite sample spaces it implies, but is not implied by, equation (1).
Parameter defined by equation (13).
By Equation 1.11, we obtain.
These values are given by Equation (3).
where Φ is defined by equation (3.2).
ESCB is obtained by Equation (4).
This probability is obtained by Equation (10).
It is shown by Equation (7).
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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