given a set of orthogonal polynomials with respect to a certain measure w(x)(adsbygoogle = window.adsbygoogle || []).push({});

[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(1-xM)> [/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 ??

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# How to prove this

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