Laurent

Related BrainMass Solutions

• Laurent Series for a Complex-Valued Function

  Discuss the convergence and divergence sets of each of those Laurent series.

• Laurent expansions

  74271 Laurent Expansion Description (See attached file for full problem description) --- Find the Laurent expansion for ? centered at z=0 ? centred at z=3 ? centred at z=3 --- Please see the attached file.

• 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).

• Laurent series

  Find the Laurent series.... solution attached This provides an example of finding the Laurent series for an annulus.

• Punctured Disk : Poles, Taylor Series, Laurent Series and Power Series

  36770 Poles, Taylor Series, Laurent Series and Power Series Suppose that a function F(s) has a pole of order m at s=s0, with a Laurent series expansion ... in the punctured disk 0<|s - s0|

• Quotient Rings, Laurent Series and Power Series

  102993 Quotient Rings, Laurent Series and Power Series If F is a field, prove that the field of fractions of F[[x]] is the ring F((x)) of formal Laurent series.

• sum from n = 1 to infinity of 1/n^(2p )

  So, all we have to do is compute the Laurent expansion of pi^2/sin^2(pi z).

• Complex Variables, Laurent Series and Uniform Convergence

  128640 Complex Variables, Laurent Series and Uniform Convergence (1) Let G = {z : 0 < abs(z) < R} for some R > 0 and let f be analytic on the punctured disk G with Laurent Series f(z) = sum a_n*z^n (from n = -oo to oo).

• Isolated singularity proof

  Prove directly from the integral formula for the Laurent coefficients that for all j = 1,2,3,..., i.e. must have a removable singularity at .