A combined symbolic and numerical algorithm for the computation of zeros of orthogonal polynomials and special functions
نویسندگان
چکیده
A Maple algorithm for the computation of the zeros of orthogonal polynomials (OPs) and special functions (SFs) in a given interval [x1, x2] is presented. The program combines symbolic and numerical calculations and it is based on fixed point iterations. The program uses as inputs the analytic expressions for the coefficients of the three-term recurrence relation and a differencedifferential relation satisfied by the set of OPs or SFs. The performance of the method is illustrated with several examples: Hermite, Chebyshev, Legendre, Jacobi and Gegenbauer polynomials, Bessel, Coulomb and Conical functions. © 2003 Elsevier Science Ltd. All rights reserved.
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عنوان ژورنال:
- J. Symb. Comput.
دوره 35 شماره
صفحات -
تاریخ انتشار 2003