complex mean-value theorem
Theorem [1]
Suppose is an open convex set in ,
suppose is a holomorphic function , and
suppose are distinct points in .
Then there exist points on (the straight line
connecting and not containing the endpoints
), such that
where and are the real (http://planetmath.org/RealPart) and imaginary parts of
a complex number
, respectively.
References
- 1 J.-Cl. Evard, F. Jafari, A Complex Rolle’s Theorem, American Mathematical Monthly, Vol. 99, Issue 9, (Nov. 1992), pp. 858-861.
Title | complex mean-value theorem |
---|---|
Canonical name | ComplexMeanvalueTheorem |
Date of creation | 2013-03-22 13:49:02 |
Last modified on | 2013-03-22 13:49:02 |
Owner | matte (1858) |
Last modified by | matte (1858) |
Numerical id | 7 |
Author | matte (1858) |
Entry type | Theorem |
Classification | msc 26A06 |