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Direct spreading measures of Laguerre polynomials. (English) Zbl 1223.33017
The authors study the spreading measures of the Rakhmanov probability density \(\rho _{n, \alpha }(x) = \frac{1}{d^2_n}x^{\alpha }e^{-x}[L^{(\alpha )}_n(x)]^2\) along the positive real line for the Laguerre orthogonal polynomials. In particular, they study the standard deviation, Fisher information, Renyi and Shannon entropies as well as the so-called \(q\)-Renyi and Shannon lengths. They use several methods for their computation and also present some numerical results to illustrate the sharpness of their estimates.

MSC:
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
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