Let {λj}∞j=1 be a strictly increasing sequence of positive numbers with λ1 = 1. We find a simple explicit formula for the orthogonal Dirchlet polynomials {φn} formed from linear combinations of { λ j n j=1 , associated with the arctangent density. Thus ∫ ∞ −∞ φn (t)φm (t) dt π (1 + t2) = δmn. We obtain formulae for their Christoffel functions, and deduce their asymptotics, as well as universality limits, and spacing of zeros for their reproducing kernels. We also investigate the relationship… CONTINUE READING