Obtaining an Orthogonal Basis

In order for the basis to be orthogonal, it is necessary that the following two conditions hold  

Combining Eqs. (4.37) and (4.38) gives that for the case of an even power the individual experimental coefficients can be written as 

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In order to obtain an orthogonal basis in this case, it is necessary to note that the results from Sect. 4.7 need to be modified to take into consideration the fact that an arbitrary number of experiments will be performed. In this case, the key constraint can be written as... 

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