- #1
zetafunction
- 391
- 0
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 ??
[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 ??