
#1
Nov1809, 01:21 PM

P: 399

given a set of orthogonal polynomials with respect to a certain measure w(x)
[tex] \int_{a}^{b}dx w(x) P_{n} (x)P_{m} (x) = \delta _{n,m}h_{n} [/tex] how can anybody prove that exists a certain M+M Hermitian matrix so [tex] P_{m} (x)= < Det(1xM)> [/tex] here <x> means average or expected value of 'x' if we knew the set of orthogonal polynomials [tex] P_{m} (x) [/tex] for every 'm' and the measure w(x) , could we get the expression for the matrix M ?? 



#2
Nov1809, 02:10 PM

P: 608

Your equation doesn't make much sense to me. How about providing an example. A particular orthogonal system and the corresponding matrix.




#4
Jan510, 12:12 PM

P: 3

How to prove this
Interesting way to react to posts that do not tickle the own ears  delete them. You guys are not seekers of truth. Ibn al Haytham would be ashamed for you all.



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