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Mar 17, 2016 at 18:09 comment added Hosein Rahnama I updated my question details. Can you help to go further with it? :)
Mar 17, 2016 at 17:30 comment added BlacKow I kinda see what you want... You want some sort of analytical proof made by Mathematica.. I'm not sure if it's a good tool for that. I will be interested to see other answers.
Mar 17, 2016 at 17:24 comment added Hosein Rahnama In $A$, you just used the final formula. I want to obtain this formula with Mathematica. Yes, I want the intermediate steps.
Mar 17, 2016 at 17:22 comment added BlacKow My A does precisely (1) and (2). You want to see intermediate steps how Mathematica figured out the integral "used orthogonality"?
Mar 17, 2016 at 17:18 comment added Hosein Rahnama As I stated in my question, I want to start from $(1)$, do the regular arithmetic that we both know and obtain $a_i$ and $b_i$. That is all I want. But I just want to write a code for it. :)
Mar 17, 2016 at 17:17 comment added BlacKow The formula comes directly from definition of metrics. When you call something orthogonal you do this in regards to the metrics (or inner product definition). You can ask Mathematica to check if selected set of functions is orthogonal in regards to metrics.
Mar 17, 2016 at 17:13 comment added Hosein Rahnama (+1) Thanks for the attention. I know the final formula but I want to obtain it by Mathematica. :)
Mar 17, 2016 at 17:09 history answered BlacKow CC BY-SA 3.0