Term used to describe a complex function that is differentiable at every point in a region
1
If a complex function is analytic at all finite points of the complex plane, that function is said to be _________.
1
If a function is analytic in a region, then in that region it satisfies these equations
2
If f(z)=u+iv is analytic in region, then u and v satisfy what famous differential equation?
2
This theorem says that the contour integral around a closed curve of an analytic function is zero
2
A point at which a function is not analytic
1
In any neighborhood of an essential singularity, however small, an analytic function assumes every value in the complex plane with at most one exception
2
An analytic function f is said to have a ______ of order n at a point z=a if all terms in the Laurent series for which m is less than -n vanish & the -n term does not equal zero
1
Concept
Name of Concept or Theorem
Number of words
A function whose only singularities, other than the point at infinity, are poles is called_________.
1
A unique series expansion of a complex function in positive and negative powers
2
The coefficent of the 1/(z-a) term in the Laurent series of a function f(z) is called the _______.
1
This powerful theorem allows one to evaluate contour integrals of functions which are analytic except at a finite number of poles
2
This theorem says that any bounded entire function must be constant
2
A point in the complex plane whose complex argument can be mapped from a single point in the domain to multiple points in the range
2
A transformation in the complex plane that preserves local angles is said to be
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