On the Roots of the Legendre Laguerre, and Hermite Polynomials

 S. Álvarez-Ballesteros, J. López-Bonilla, R. López-Vázquez,
ESIME-Zacatenco, Instituto Politécnico Nacional, Edif. 5, 1er. Piso, Col. Lindavista CP 07738, CDMX, México

ABSTRACT. For several orthogonal polynomials, Cohen proved that their roots are the eigenvalues of symmetric tridiagonal matrices. In this paper, we give examples of this Cohen’s result for the Legendre, Laguerre, and Hermite polynomials, which are useful in applications to quantum mechanics and numerical analysis.

KEYWORDS: Laguerre and Hermite polynomials, Leverrier-Takeno’s technique, Legendre polynomials.



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