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On the polynomial solutions of ordinary differential equations of the fourth order
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The density of zeros of polynomial solutions of ordinary differential equations of the fourth order with coefficients depending only on the independent variable is analyzed. The first four moments of such a density are given directly in terms of the coefficients which characterize the differential operator. Application to the nonclassical orthogonal polynomials corresponding to the names Krall–Legendre, Krall–Laguerre, and Krall–Jacobi is done. Global asymptotic properties of the zeros of these polynomials are also obtained.
Title: On the polynomial solutions of ordinary differential equations of the fourth order
Description:
The density of zeros of polynomial solutions of ordinary differential equations of the fourth order with coefficients depending only on the independent variable is analyzed.
The first four moments of such a density are given directly in terms of the coefficients which characterize the differential operator.
Application to the nonclassical orthogonal polynomials corresponding to the names Krall–Legendre, Krall–Laguerre, and Krall–Jacobi is done.
Global asymptotic properties of the zeros of these polynomials are also obtained.
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