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Sturm-Liouville orthogonality

The fact that eigenfunctions of a regular Sturm-Liouville problem belonging to distinct eigenvalues are orthogonal, once the weight function is included.

Sturm-Liouville orthogonality states that if y_m,y_n are eigenfunctions of a regular Sturm-Liouville problem with distinct eigenvalues \lambda_m\neq\lambda_n, then \displaystyle\int_a^b\sigma(x)y_m(x)y_n(x)\,dx=0 -- the trigonometric orthogonality relations of ch.03 are the special case p\equiv\sigma\equiv1, q\equiv0.

See also

Sturm-Liouville problem weight function (Sturm-Liouville)
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