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.
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(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 ...
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.