Use the orthogonality relation to find expressions for the coefficients in the eigenfunction expansion of a function f(x):

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- May 4th 2010, 11:17 AMArythEigenfunction Expansion
Use the orthogonality relation to find expressions for the coefficients in the eigenfunction expansion of a function f(x):

- May 4th 2010, 11:19 AMBruno J.
Hint : what is ?

- May 4th 2010, 11:40 AMAryth
Isn't it: ?

Sorry if I don't understand how it helps... I do know that is a quotient of inner products... I'm afraid I don't know how to show it. - May 4th 2010, 11:48 AMBruno J.
- May 4th 2010, 11:56 AMAryth
Ok... So... We get:

Which means that:

Is that along the right lines? - May 4th 2010, 12:04 PMBruno J.
- May 4th 2010, 12:05 PMAryth
Ah, I see. I appreciate the help. Thanks a lot.

- May 4th 2010, 12:06 PMBruno J.