. (a) Find the Fourier series for the 27-periodic function given by ƒ(x) = x³ — π²x, (b) The Riemann zeta function is defined as G(s) = n=1 -π < x < π. ns Use (a) and Parseval's theorem to evaluate (6).
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- 1. Find the Fourier series of the given function f(x), which is assumed to have the period 2. a. f(x)=x² (π < x1. What is a Fourier series representation of the function (1) 2 in the range -π < x < π? f(x) = ln secConsider the piecewise function x, -2 0. (v) Find the simplified general expression for the Fourier coefficients bn, n > 0. (vi) What is the Fourier series F(x) of f(x)? (vii) What value will the Fourier series compute to at x = 18? viii) What is the overall convergence rate of the Fourier series?5. Convert the function f(x)=eux and f(x+2) = f(x) defined in the interval (-π < x < π) to the complex Fouriér Series.Q2.A. Sketch a graph of f(x), then find the Fourier series of f(x) for three values and has a period of 27. f(x) = { 1²/2 01. Find The Fourier series for the function defined by 0Recommended 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,