In the interval (-pi, pi), δn(x) = (n/x^1/2) e ^(-n^2 x^2)
a) Expand δn(x) as a Fourier Cosine Series.
b) Show that your Fourier Series agrees with a Fourier expansion of δn(x) in the limit as n--> infinity.
Please see the attached file for the fully formatted problems.© BrainMass Inc. brainmass.com October 24, 2018, 6:22 pm ad1c9bdddf
I am including a short overview of Fourier series you can pretty much read past if you have seen it before. I found that expanding the exp(x^2) function in a Maclauren power series seemed to be the most profitable in obtaining values for the definite integrals. The values in the powers of m for the series expansion have ...
Fourier Cosine Series and Fourier Series Expansion are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.
Fourier Series Expansion: Example Problem
Please see the attached file for the fully formatted problems.
See f(x) in the file.
1. Sketch f(x) over -3<x<3
2. Is f(x) odd, even or neither?
3. Solve for the Fourier coefficients.
4. Write out the Fourier series expansion up to n=3