How can one find the Fourier series of f(x)=x^3 -(pi^2)*x based on knowing the cosine Fourier series for f(x)=x? I first did it using the x series in sines and integrating it twice, and that comes out easily, but can't understand how to do it starting with the cosines version of f(x)=x, which is given as x =pi/2 + sum [(2[-1^n)-1] cos(nx)/(pi*n^2)]
How can one find the Fourier series of f(x)=x^3 -(pi^2)*x based on knowing the cosine Fourier series for f(x)=x? I first did it using the x series in sines and integrating it twice, and that comes out easily, but can't understand how to do it starting with the cosines version of f(x)=x, which is given as x =pi/2 + sum [(2[-1^n)-1] cos(nx)/(pi*n^2)]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
How can one find the Fourier series of f(x)=x^3 -(pi^2)*x based on knowing the cosine Fourier series for f(x)=x? I first did it using the x series in sines and integrating it twice, and that comes out easily, but can't understand how to do it starting with the cosines version of f(x)=x, which is given as x =pi/2 + sum [(2[-1^n)-1] cos(nx)/(pi*n^2)]
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 4 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Similar questions
- 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:WILEYAdvanced 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,