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How to prove this

by zetafunction
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zetafunction
#1
Nov18-09, 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(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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g_edgar
#2
Nov18-09, 02:10 PM
P: 607
Your equation doesn't make much sense to me. How about providing an example. A particular orthogonal system and the corresponding matrix.
Dragonfall
#3
Dec31-09, 02:36 PM
Dragonfall's Avatar
P: 995
Quote Quote by mathaino View Post
I recommend "proof by believe", i.e. write something that looks like a proof, believe it is a correct proof, without being able to check whether it is correct.
Looks like we got ourselves a troll.

mathaino
#4
Jan5-10, 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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