# Eigenfunctions, Eigenvalues, Harmonic Functions and Sturm-Liouville Problems

Given the equation below find the eigenvalues and then the eigenfunctions. Compute the coefficients of the eigenfunction expansion. In each case determine what the eigenfunction expansion converges to on the interval and the sum of the first N terms on the same set of axes for the given interval.

Please show the function (N=5) and how it is expanded!!

f(x) = x^2 x is greater than or equal to -3 Pi or less than or equal to 3 Pi

y(-3Pi) = y(3Pi)..... y(-3Pi) = y(3Pi)

y'' + y = 0

© BrainMass Inc. brainmass.com October 9, 2019, 7:15 pm ad1c9bdddfhttps://brainmass.com/math/linear-algebra/eigenfunctions-eigenvalues-harmonic-functions-and-sturm-liouville-problems-112537

#### Solution Preview

Hello and thank you for posting your question to BrainMass!

For generality sake, I ...

#### Solution Summary

Eigenfunctions, Eigenvalues, Harmonic Functions and Sturm-Liouville Problems are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.