proof of Riemann’s removable singularity theorem
Suppose that is holomorphic on and . Let
be the Laurent series of centered at . We will show that for , so that can be holomorphically extended to all of by defining .
For any non-negative integer , the residue of at is
This is equal to zero, because
because the constant term in the power series of is zero.
for some . This implies that as , so is a removable singularity of .
|Title||proof of Riemann’s removable singularity theorem|
|Date of creation||2013-03-22 13:33:03|
|Last modified on||2013-03-22 13:33:03|
|Last modified by||pbruin (1001)|