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Orthogonality Of Eigen Functions

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Orthogonality Of Eigen Functions :- Definition :          Two distinct continuous functions f   and φ on [a,b] are said to be orthogonal with respect to a continuous weight function γ if                           b                          ∫ f(x) φ(x) γ(x) dx = 0  ...(14)                          a    An infinite set of functions defined on [a,b] is to be an orthogonal system with respect to the weight function γ on [a,b] if every pair of distinct functions of the set are orthogonal with respect to γ .  Example :         The set of functions {φₙ} ,      where φₙ(x) = sin nx , n=1,2,.... on [0,π] is an orthogonal system with respect to the weight function having th...