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

Related BrainMass Solutions

• Singular Point : Pole and Residue

  TO find the residue we have: B= lim ((z-1)^2*exp(2z)/(z-1)^2)'= lim (exp(2z))'= 2exp(2) z--->1 z--->1 Poles and residues are investigated. The functions for singular points are given.

• 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

• Summation from minus infinity to infinity of 1/(n^4 + a^4)

  The contour integral of f(z) g'(z)/g(z) dz tends to zero for R to infinity if |f(z)| tends to zero faster than 1/|z|, the summation of f(z) over the integers then equals minus the sum over the residues of f(z) pi cot(pi z) at the poles of f(z).

• 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.

• Complex integrals

  (2) We use the theorem of residues: For integrating a function counter-clockwise over a closed contour, int(dz f(z)) = 2 Pi i Sum(a(c)) where the sum is over the singular points, c, within the contour, and the residue, a(c), is the (-1)st coefficient

• Momentum space representation of a wavefunction.

  If a function has a singularity at z = z0 and has an expansion around that point of the form: a_n/(z-z0)^n + a_{n-1}/(z-z0)^(n-1)+ ... + r/(z-z0) then the residue at z0 is defined as r, i.e. the coefficient of 1/(z-z0).

• Determine the singular points of the function

  33526 Determine the singular points of the function In each case, determine the singular points of the function and state why the function is analytic everywhere except at those points: (a) f (z) = (2z + 1) / [z (z^2 + 1)] (b) f (z) = (z^3 + i) /

• Laurent

  29288 Find the Laurent Find the Laurent series about all singular points of f(z) = 1/(z(z+1)^2) {See attachment}. Please see the attachment. This solution shows how to find a Laurent series about singular points.

• Rearranging Expressions and Residues (Find the two singular points and the residue for each : exp(tz)/(z2 + 2z +17) (t>0))

  Residues and rearranging equations are investigated. Two singular points and the residues are found.