Sturm-Liouville expansion
Please show each step of your solution. When you use theorems, definitions, etc., please include in your answer.
3. Expand... in terms of the eigenfunctions of the Sturm-Liouville problem.
Please see attached.
© BrainMass Inc. brainmass.com March 4, 2021, 6:25 pm ad1c9bdddfhttps://brainmass.com/math/fourier-analysis/sturm-liouville-expansion-44174
Solution Preview
Hello and thank you for posting your question to Brainmass!
The solution is attached below (next to the paperclip icon) in two formats. one is in Word XP Format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.
(The first 3 non-vanishing terms, not the first four non-vanishing terms)
(H(x) denotes Heaviside Step Function. We can take any Heaviside Step Function.)
(The problem is from Periodic and Singular Sturm-Liouville Problems.)
This is the famous Sturm-Liouville equation that leads to the Legendre's polynomials.
The equation can be written as:
The general orthogonality of the eigenfunctions:
Assume the general form of Sturm-Liouville equation:
Define two eigenfunctions which ...
Solution Summary
This shows how to expand a function in terms of the eigenfunctions of a given Sturm-Liouville problem and plot the function and the sum of the first three nonvanishing terms.