proof of complex mean-value theorem
The function is a function defined on [0,1]. We have and . By the ordinary mean-value theorem, there is a number , , such that . To evaluate , we use the assumption that is complex differentiable (holomorphic). The derivative of is equal to , then , so satisfies the required equation. The proof of the second assertion can be deduced from the result just proved by applying it to the function f multiplied by i.
|Title||proof of complex mean-value theorem|
|Date of creation||2013-03-22 14:34:39|
|Last modified on||2013-03-22 14:34:39|
|Last modified by||Wolfgang (5320)|