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By multiplying both sides by P(N), which is between 0 and 1.
So multiplying both sides of the Fourier series and then doing the integration leads us, after the appropriate manipulation, to the expression that I have up here.
Multiplying both sides of.
Multiplying both sides of (3.41).
Then, by multiplying both sides of Eqs.
Multiplying both sides of (3.6) by (3.8).
Multiplying both sides of (2.3) by, then (2.5).
Multiplying both sides of (3.5) by, we have.
By multiplying both sides of (1.9) by, we get (2.11).
Multiplying both sides of (2.16) by, we have (2.17).
Multiplying both sides of (3.12) by, one has (3.13).
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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