Functional equations and electrostatic models for orthogonal polynomials
The author has written an interesting survey paper on the connections between orthogonal polynomials, the functional equations they satisfy and some extremal problems. NEWLINENEWLINENEWLINEThe zeros of the orthogonal polynomials arise as solutions to electrostatic problems with respect to a logarithmic potential and there is an intimate connection between the discriminant of the orthogonal polynomial and the coefficients arising in a degree reducing differential recurrence relation of the type NEWLINE\[NEWLINE\frac {d}{dx} p_n(x)=A_n(x)p_{n-1}(x)-B_n(x)p_n(x).NEWLINE\]NEWLINE Also generalizations to other linear degree reducing operators are discussed.NEWLINENEWLINEFor the entire collection see [Zbl 0967.00059].
scientific article; zbMATH DE number 1683611