Isolated Singularities Discussed

Related BrainMass Solutions

• Isolated singularities

  This shows how to classify all the isolated singularities of functions. The reasoning of each classifications are discussed.

• Zeroes of functions

  It has removable singularities at with order and the corresponding value is , where is any integer. It also has isolated singularities at with order 1. This shows how to locate all zeros and singularities for functions.

• Isolated singularities

  This provides an example of classifying isolated singularities.

• 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?

• 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.

• 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.

  58903 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)| = infinity Now, prove that a function f has an essential singularity

• Isolated singularity proof

  and removable singularities.

• Laurent series expansion of complex functions

  (1.1) There are two singularities for this function, namely and .

• Residues, essential singularities and integrals

  392500 Residues, essential singularities and integrals 1. Find where is the function f(z) = 1/((2z-1)(Log(2z)) analytic, and then find all residues in all isolated singular points. 2.