Dirichlet orthogonal polynomials with Laguerre weight

Let {λj}j=1∞ be a sequence of distinct positive numbers. We find explicit formulae for the orthogonal Dirichlet polynomials {ψn}{ψn} formed from linear combinations of {λj−it}j=1n, associated with the Laguerre weight. Thus ∫0∞ψn(t)ψm(t)¯e−tdt=δmn. In addition, we estimate Christoffel functions and establish Markov–Bernstein inequalities.