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The phrase "approximation for the argument" is correct and usable in written English.
It can be used in contexts where you are discussing a method or value that serves as a close estimate for a particular argument or variable in a mathematical or logical discussion.
Example: "In our calculations, we used an approximation for the argument to simplify the equation and make it more manageable."
Alternatives: "estimate for the argument" or "approximate value for the argument".
Exact(1)
One possible limitation is the linear approximation for the argument of the nonlinear regulation function g.
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Now for the argument about surnames!
Are these sources appropriate for the argument?
The Fresnel integrals in the diffraction analyses of Penny and Price [Penny, W.G., Price, A.T., 1944. Diffraction of water waves by breakwaters. Misc. Weapons Development Technical History 26, Artificial Harbors, Sec. 3D; Philos. Trans. R. Soc. London, Ser. A, 244 (1952) 236] are replaced by polynomial approximations for positive arguments in the range of zero to infinity.
IAA for the arguments is more interesting.
The Broadway League used approximations for the end-of-year grosses — the most recent season began May 26 , 2008 and ended May 24 , 2009
In addition, steady-state solutions for both CHT and CRT are also developed based on the approximation for Bessel functions with very small argument values.
Such approximation is valid only for relatively small values of the argument (pressure P in this case), If for experimental data notable distortion from such simple relation appears one should use the functional, experimental form (preferably).
Moreover, the sum of Rayleigh fading used in the derivation of BER is only an approximation valid for small arguments only.
Most of these methods are based on numerical approximations and are valid for a certain range of the argument value.
The argument for the plan is straightforward.
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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