On the Roots of the Legendre Laguerre, and Hermite Polynomials
DOI:
https://doi.org/10.51200/bsj.v38i2.4415Keywords:
Laguerre and Hermite polynomials, Leverrier-Takeno’s technique, Legendre polynomialsAbstract
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.
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