proof of the Cauchy-Riemann equations
Existence of complex derivative implies the Cauchy-Riemann equations.
Suppose that the complex derivative
exists for some . This means that for all , there exists a , such that for all complex with , we have
The Cauchy-Riemann equations imply the existence of a complex derivative.
Suppose that the Cauchy-Riemann equations
with a similar relation holding for . Combining the two scalar relations into a vector relation we obtain
we can therefore rewrite the above limit relation as
which is the complex limit definition of shown in (1).
|Title||proof of the Cauchy-Riemann equations|
|Date of creation||2013-03-22 12:55:39|
|Last modified on||2013-03-22 12:55:39|
|Last modified by||rmilson (146)|