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Exact(32)
Substituting the value A in (2.4), we get (2.2).
Substituting the value of (T^=2.73841) in Eqs.
Substituting the value of into (2.10) and (2.13), we obtain (2.7).
On substituting the value of ( P_{ Y+ S} (2) ) in Eqs.
Substituting the value of c 0 in (2.4), we obtain (2.3).
Substituting the value of (b_{2}) in (2.5), we get the solution (2.2).
Similar(28)
The objective function is then evaluated by substituting the values of the xi in the equation that defines f.
Substituting the values of and in (2.6), we obtain (2.5).
Further, substituting the values of a and b, we have.
Therefore, in both, (3.29) and (3.32), and the result now follows by substituting the values, (3.40).
Substituting the values of (c_{0}) and (c_{m-1}) in (2.3), we obtain the result.
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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