Let be a domain.
The second definition makes sense since a meromorphic functions has only isolated poles, and thus is defined by the first equation when we are close to . Some basic properties of the spherical derivative are as follows.
If is a meromorphic function then
is a continuous function,
for all .
Note that sometimes the spherical derivative is also denoted as rather then .
- 1 John B. Conway. . Springer-Verlag, New York, New York, 1978.
- 2 Theodore B. Gamelin. . Springer-Verlag, New York, New York, 2001.
|Date of creation||2013-03-22 14:18:36|
|Last modified on||2013-03-22 14:18:36|
|Last modified by||jirka (4157)|