Find Laurent series function f(z) for given intermediate circle 1 < |z| < 3 if f(z) = 1/((z - 1)*(z - 3))
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Find Laurent series function f(z) for given intermediate circle 1 < |z| < 3 if
f(z) = 1/((z - 1)*(z - 3))
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- 11. (a) Find the Fourier series of the 27-periodic function given on the interval -<< π by f(x) = sinx. (b) Plot several partial sums to illustrate the convergence of the Fourier series.+00 +00 Let Jo(x) = >(-1)" and J1(x) = >(-1)"- 2n+1 n=0 n!n!22n n=0 n!(n +1)!22n+1 The functions Jo and J1 are called Bessel functions of the first kind of orders zero and one, respectively, and both converge for all real values of x. Show that Jo'(x) =-J1(x).If f(x) = 4,0+3 - n2 (a) Page 3 of 11 (0) Module code: CAPE200001 (ii) (ii) Using the power series expansion for exp(-x) or otherwise, find the first 3 non-zero terms in the power series expansion of exp(-2x¹). Remember that exp(-x) is the same as e. Calculate lim Use the power series from (i) to find the limit of 1-2²-e 1-exp(-2x¹) Turn the page over using l'Hôpital's rule. 2²-exp(-2²) as x→0.period -π ≤ t ≤ π. The following f(t) is a periodic function of period T = 27, defined over the -2 2 when when 0 < t ≤π -= Finding the residue with Laurent series expansion for two of the following functions: (1) (2²-2z+2)/(z-2) in the domain |z - 1| < 1. (2) 1) in the domain 0 < |z − 1| < 1. (3) (2-1) sin around z = -2.Let f(z) be a complex function. Fnd the Laurent series for f(z) = 1/((z^2 - 4)(z-2)) centered at z=2 and specify in which it converges.Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,