for some , , and all with sufficiently large is necessarily equal to a polynomial function.
Liouville’s theorem is a vivid example of how stringent the holomorphicity condition on a complex function really is. One has only to compare the theorem to the corresponding statement for real functions (namely, that a bounded differentiable real function is constant, a patently false statement) to see how much stronger the complex differentiability condition is compared to real differentiability.
|Date of creation||2013-03-22 12:04:31|
|Last modified on||2013-03-22 12:04:31|
|Last modified by||djao (24)|