Consider the Sturm-Liouville problem

Given the eigenfunctions of this boundary value problem are .
Using this as an orthonormal basis, which of the following is the eigenfunction expansion of

Question

Consider the Sturm-Liouville problem

Given the eigenfunctions of this boundary value problem are  .
Using this as an orthonormal basis, which of the following is the eigenfunction expansion of

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The Answer of Consider the Sturm-Liouville problem

Given the eigenfunctions of this boundary value problem are  .
Using this as an orthonormal basis, which of the following is the eigenfunction expansion of

Consider the Sturm-Liouville Problem