کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4640236 1341268 2011 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Direct spreading measures of Laguerre polynomials
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Direct spreading measures of Laguerre polynomials
چکیده انگلیسی

The direct spreading measures of the Laguerre polynomials Ln(α)(x), which quantify the distribution of its Rakhmanov probability density ρn,α(x)=1dn2xαe−x[Ln(α)(x)]2 along the positive real line in various complementary and qualitatively different ways, are investigated. These measures include the familiar root-mean square or standard deviation and the information-theoretic lengths of Fisher, Renyi and Shannon types. The Fisher length is explicitly given. The Renyi length of order qq (such that 2q∈N2q∈N) is also found in terms of (n,α)(n,α) by means of two error-free computing approaches; one makes use of the Lauricella function FA(2q+1)(1q,…,1q;1), which is based on the Srivastava–Niukkanen linearization relation of Laguerre polynomials, and another one utilizes the multivariate Bell polynomials of Combinatorics. The Shannon length cannot be exactly calculated because of its logarithmic-functional form, but its asymptotics is provided and sharp bounds are obtained by the use of an information-theoretic optimization procedure. Finally, all these spreading measures are mutually compared and computationally analyzed; in particular, it is found that the apparent quasilinear relation between the Shannon length and the standard deviation becomes rigorously linear only asymptotically (i.e. for n≫1n≫1).

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 235, Issue 5, 1 January 2011, Pages 1129–1140
نویسندگان
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