A second-order ordinary differential equation d/(d x)[p(x)(d y)/(d x)] + [λ w(x) - q(x)] y = 0, where λ is a constant and w(x) is a known function called either the density or weighting function. The solutions (with appropriate boundary conditions) of λ are called eigenvalues and the corresponding u_λ(x) eigenfunctions. The solutions of this equation satisfy important mathematical properties under appropriate boundary conditions.
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