Discrete entropies of orthogonal polynomials

Discrete entropies of orthogonal polynomials

Let $p_n$ be the $n$-th orthonormal polynomial on the real line, whose zeros are $\lambda_j^{(n)}$, $j=1, ..., n$. Then for each $j=1, ..., n$, $$ \vec \Psi_j^2 = (\Psi_{1j}^2, ..., \Psi_{nj}^2) $$ with $$ \Psi_{ij}^2= p_{i-1}^2 (\lambda_j^{(n)}) (\sum_{k=0}^{n-1} p_k^2(\lambda_j^{(n)}))^{-1}, \quad...

Celý popis

Podrobná bibliografie
Hlavní autoři: Aptekarev, A. I., Dehesa, J. S., Martínez-Finkelshtein, Andrei, Yáñez, R.
Médium: info:eu-repo/semantics/article
Jazyk:English
Vydáno: 2012
Témata:
Polinomios ortogonales
Entropía de Shannon
Chebyshev polinomios
Fórmula Euler–Maclaurin
Orthogonal polynomials
Shannon entropy
Chebyshev polynomials
Euler–Maclaurin formula
On-line přístup:http://hdl.handle.net/10835/1630

Internet

http://hdl.handle.net/10835/1630

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