Branch Cut for Log(1 - 1/z^2)

Related BrainMass Solutions

• How to Find Branch Cuts for log(f(z))

  428190 Branch cuts points of log Can you please wirte down a precise method to find the branch cuts and points of log(f(z)) for any f(z)? like what is the difference between log(z^2-1), log(1-z^2) and log(1-1/z^2) and how can you tell?

• Branch of logarithmic equation and derivative question

  Determine a branch of log that is analytic at z = -1, and find its derivative there. A branch cut is a curve (with ends either open, closed, half-open) in the complex plane across which an analytic multivalued function is discontinuous.

• Residues, essential singularities and integrals

  But the most well known case of Log(z) is atypical in that one branch point singularity is at infinity and the branch cut runs toward that point at infinity.

• Evaluating an Integral with 2nd Order Pole : Moivre-Laplace Fomulation

  The single-valued branch of the function is picked out by the cut along negative part of imaginary axis. Thus, -/2  arg z  3/2. It means that = for x  0 , and = for x  0.

• Singular points and residues of 1/[(Cosh(z))-2exp(z)]

  Then we have: y + y^(-1) - 4 y = 0 ----------> 3 y^2 = 1 ---------> y = +/- 3^(-1/2) We can then compute z using z = Log(y) + 2 pi i n where n is an integer and the logarithm is defined by taking the branch cut along some curve

• Complex Theorem for Continuous Anti-derivative

  Introduce a horizontal branch cut from z_0 to infinity as in Fig. 4.25. In the resulting "slit plane" the function 1 / (z — z_0) has the anti-derivative Log (z — z_0).

• Contour integral involving branch point singularity

  Observe that (z^2 + 1)^(-a) has branch points at z = ±i and z = infinity.) You have to define the function f(z) = (z^2+1)^(-a) as a single valued function first.

• Solve the equation sin(z) = 2

  by specifying the branch cut.

• Integral from x = 0 to infinity

  The branch cut can be taken along any line r exp(i alpha) for pi < alpha < 2 pi. So, in the lower half plane (theta would increasein value until it becomes alpha and then it would jump to alpha - 2 pi).