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The phrase "for a specific example" is correct and usable in written English.
For example, you could use it in a sentence such as "Let's take a look at a specific example to illustrate this concept."
Exact(28)
Asked for a specific example, he pointed to a repeated re-organisation of bureaucratic structures in the National Health Service, which he called "probably destabilising and wasteful".
Numerical results are presented for a specific example.
Simulation results for a specific example demonstrate the reasonableness of the analytical formulation.
This question is investigated for a specific example of dry atmospheric convection, namely the simulation of warm air bubbles.
These expressions are used to derive voltage and charge profiles for a specific example under various circumstances.
Specifically, an eigenvalue analysis is first performed, followed by computations using the finite difference method for a specific example involving a soil layer with quadratically varying material parameters.
Similar(32)
For illustration, a specific example is taken from the beverage industry (see the case-based example in Sect. 5.1).
Algorithm 1 is a specific example for these definitions (take chain 2 in Figure 4 for example).
Tungsten-copper (W-Cu) liner was selected as a specific example for the experiment design and execution in this paper.
A specific example for the regulatory role of Fas is exemplified by the response to LPS.
Validation of alternative methods for eye irritation testing is a specific example illustrating important concepts.
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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