Purchase Solution

Series and singularities of complex functions

Not what you're looking for?

Ask Custom Question

1. Find the series representations for the function
f(z) = z/[(z-2)(z^2-1)]
in powers of z that is valid when
1) |z| < 1
2) 1 < |z| < 2
3) |z| > 2

2. Fine all singularities of the function f in C, and determine whether it is a pole (find its order), a removable singularity, or an essential singularity.
1) f(z) = ze^(3/z)
2) f(z) = (cos z)/[(z - (pi/2))(sin z)]
3) f(z) = (cos z)/[(z^2)(z - pi)^3]

Purchase this Solution
Solution Summary

We give a detailed solution to the problems.

Purchase this Solution
Free BrainMass Quizzes
Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

View More Free Quizzes
Related BrainMass Solutions

  • Singularities, Convergence of Taylor Series, Residues and Contour Integral

    170579 Singularities, Convergence of Taylor Series, Residues and Contour Integral Consider the complex function: f(z) = 1/(z^2 + z + 1)(z + 5i) a) Find and classify the singularities of f(z); b) Without finding the series explicitly, determine

  • Laurent series expansion of complex functions

    561993 Laurent series expansion of complex functions For each of the functions f(z) find the Laurent Series expansion on for the given isolated singularity (specify R).

  • Singularities of functions

    Suppose the functions f and g have isolated singularities at and these singularities are poles of m and n, respectively. What can be said about the singularities of the functions f+g, f.g and f/g?

  • Complex Function Calculus

    are: (1.5) The Taylor series of the trigonometric functions around functions are: (1.6)   Since are simple poles, we can write: (1.7) By equating coefficients we obtain at (1.8) Therefore (1.9) And at (1.10

  • Derivative of a ratio of complex functions

    565410 Derivative of a ratio of complex functions Show that the derivative of g(z) exists, and hence g(z) is complex analytic, at points where g(z) does not diverge, thereby proving that the points where g(z) diverges are the only singularities. 


  • Singularities of Analytic Functions

    575777 Singularities of Analytic Functions Please see the attached file for the functions. Question: For the following function, determine the nature of the singularities (removable, pole, or essential) and calculate the residues.

  • Isolated singularities

    29329 Isolated Singularities of Functions Classify all the isolated singularities of the following functions (classify as removable, pole of order m, or essential). Explain the reasoning for each classification.

  • Zeroes of functions

    25033 Locate all Zeros and Singularities Locate all zeros and singularities for each of the attached functions. SHOW ALL WORK SHOW ALL STEPS ANSWER ALL PARTS OF THE QUESTION SEND RESPONSE AS ATTACHMENT.

  • Singularities and Poles

    120269 Singularities and Poles The function f(z) = zsin(pi/z)/[(z-1)(z-2)^2] has isolated singularities only. Determine the singularities of f(z) and classify each of them as removable, a pole, or an essential singularity.

View More Related Solutions