Let FCZ) = around 2 = 1 2+Z Determine the Laurent Series
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- prove that 1+3+5+ .. . +(2n-1) = na n=!,2,3.e pin)=D1+3+5 tove %3D +(2n-1)=n² %3DFor each of the time series models below undertake the following steps: • Write each time series in characteristic polynomial form using backshift operator (MA or AR or ARMA polynomials as required) • Factorise the relevant polynomials and find the roots of the polynomials. • You are given the following additional information regarding the relationship between stationarity and the characteristic polynomial roots. An AR(p) process is a stationary process if and only if the modulus of all the roots of the AR characteristic polynomial are greater than one. An MA(q) process is always stationary if the MA coefficients are finite. An ARMA (p,q) model admits a unique stationary solution when the AR characteristic poly- nomial and the MA characteristic polynomial have no common roots and the AR polynomial satisfies that it has no unit roots. Use this information to determine which of the below models is stationary. (Make sure to justify your answer.) (a) VY + ²3 (Yt + 5Y₁-1) = € - €t-1 − −2+ 3…Please show me the working out for Q1 and Q2.
- 34) find the Maclaurin series for fC2)= COs 32Question 2 Determine the taylor series of: e" No answer text provided. 1+x+x^2/2+x^3/3+... 1+x+x^2+x^3+... 1+x+(x^2)/2+(x^3)/6+...Find Launet series nepubatetion of 2(3) Let p be a prime. Show that Z = Zp\ {0}.Find the Laurent series for 2 4) (z — partial fractions on (z - - 6) 2 4)(z - 6) on the annulus 4 < |z| < 6. (Hint: First use b to write it in the form a z - 4 + 2 6in the interva) -2stRecommended 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,