Difference between revisions of "Linear fraction"
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$(2) ~ ~ ~ \displaystyle A+B z= \lim_{M\rightarrow \infty} \frac{M A+ M B}{M+z}$ |
$(2) ~ ~ ~ \displaystyle A+B z= \lim_{M\rightarrow \infty} \frac{M A+ M B}{M+z}$ |
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| + | where the expression of the function under the limit operation is expressed in a form that corresponds to (1). |
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==Inverse function== |
==Inverse function== |
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Revision as of 14:15, 31 August 2013
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).