Fourth-order differential equation satisfied by the associated of any order of all classical orthogonal polynomials. A study of their distribution of zeros
A program built in the symbolic language of Mathematica is given, which is able to calculate the unique differential equation satisfied by the associate (of any order) of one of the four classical systems of polynomials (Jacobi, Hermite, Laguerre, Bessel). The associates are polynomials satisfying the same 3-term recurrence relation as the original system of polynomials, but with shifted coefficients. The differential equation is used to study the distribution of the zeros of the associated polynomials via Newton sum rules.
scientific article; zbMATH DE number 540482
scientific article