Complex Analysis / Singularities : Now, prove that a function f has an essential singularity at z = a iff neither of the above holds for any real number s.
Not what you're looking for?
One can classify isolated singularities by examining the equations:
lim (z -> a) |z - a|^s |f(z)| = 0
lim(z -> a) |z - a|^s |f(z)| = infinity
Now, prove that a function f has an essential singularity at z = a iff neither of the above holds for any real number s.
Purchase this Solution
Solution Summary
Singularites are investigated. The solution is detailed and well presented.
Solution Preview
Please see the attached file for the complete solution.
Thanks for using BrainMass.
complex analysis/ singularities.
________________________________________
One can classify isolated singularities by examining the equations:
lim (z -> a) |z - a|^s |f(z)| = 0
lim(z -> a) |z - a|^s |f(z)| = ...
Purchase this Solution
Free BrainMass Quizzes
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Probability Quiz
Some questions on probability