functional analysis – What is the definition of asymptotically flat convergence?

I’m reading an article about a sliding modes control approach which mentions that a given function Ln(cosh(*)) is nearly linear outside the small neighborhood of the origin but partial asymptotically flat near zero.

I’m not quite sure what does “partially flat” means, I thought it might be a reference to a certain kind of convergence rate or maybe the smoothness of the function. Do you have any ideas?