ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
It is shown that for polynomial eigenfunctions of an ordinary polynomial differential operator with coefficients depending only on the independent variable it is possible to determine the density of nodes around the mean without solving the corresponding eigenvalue problem. This is done by means of the first few moments, which can be directly expressed in terms of the above-mentioned coefficients. Also, very simple expressions for the asymptotic values (i.e., when the degree of the polynomial becomes very large) of these quantities are found. For illustration, these results are applied to various orthogonal polynomials, which satisfy ordinary differential equations of second, fourth, and/or sixth order.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.526743
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