Recurrence Relation and Differential Equation for a Class of Orthogonal Polynomials

Given real number s > -1/2 and the second degree monic Chebyshev polynomial of the first kind (T) over cap (2)(x), we consider the polynomial system {p(k)(2,s)} "induced" by the modified measure d sigma(2,s) (x) = vertical bar(T) over cap (2)(x)vertical bar(2s) d sigma(x) = 1/root 1 - x(2) dx is the Chebyshev measure of the first kind. We determine the coefficients of the three-term recurrence relation for the polynomials p(k)(2,s) (x) in an analytic form and derive a differential equality, as well as the differential equation for these orthogonal polynomials. Assuming a logarithmic potential, we also give an electrostatic interpretation of the zeros of p(4 nu)(2,s) (x)(nu is an element of N)