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ok, so my math text for PDE's states the following theorem: $$f(x) = \sum_n a_n \phi_n (x)$$ for "nice enough" functions. however, the next theorem states that ##\phi_n (x)## and ##\phi_m (x)## are orthogonal relative to a weight function, ##\sigma(x)##. in other words, $$\int_\Omega \phi_n(x) \phi_m(x) \sigma(x) dx = 0 : m \neq n$$

can someone explain why this would be zero?

thanks!

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# Sturm-louville question

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