# How to prove this

1. ### zetafunction

399
given a set of orthogonal polynomials with respect to a certain measure w(x)

$$\int_{a}^{b}dx w(x) P_{n} (x)P_{m} (x) = \delta _{n,m}h_{n}$$

how can anybody prove that exists a certain M+M Hermitian matrix so

$$P_{m} (x)= < Det(1-xM)>$$ here <x> means average or expected value of 'x'

if we knew the set of orthogonal polynomials $$P_{m} (x)$$ for every 'm' and the measure w(x) , could we get the expression for the matrix M ??

2. ### g_edgar

607
Your equation doesn't make much sense to me. How about providing an example. A particular orthogonal system and the corresponding matrix.

3. ### Dragonfall

Looks like we got ourselves a troll.

4. ### mathaino

3
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.