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is zero. Whether or not two particularfunctions are orthogonal depends on how their inner product has been defined. A typical definition of an inner product for functions is
with appropriate integration boundaries. See also Hilbert space for more background.
Solutions of linear differential equations with boundary conditions can often be written as a weighted sum of orthogonal solution functions (a.k.a. eigenfunctions).
Examples of sets of orthogonal functions:
See also: orthogonal polynomials.