Linear fraction

Linear fraction is meromorphic function that can be expressed with

$(1) ~ ~ ~ \displaystyle T(z)=\frac{u+v z}{w+z}$

Linear function

Definition (1) excludes the case of linear function. However, this the linear function can be realized in limit

$(2) ~ ~ ~ \displaystyle A+B z= \lim_{M\rightarrow \infty} \frac{M A+ M B}{M+z}$

where the expression of the function under the limit operation is expressed in a form that corresponds to (1).