The Lebesgue constants of the biorthonormal system {Pn,Qn} and “Jackson” type theorem for a kind of new approximation problem

In this paper first we discuss the Lebesgue constants of the biorthonormal system {P_n,Q_n} on an ellipse, where P_n, Q_n are the Legendre polynomials and the second kind Legendre functions respectively. Secondly, for a kind of new approximation problem we give a corresponding “Jackson” type theorem of continuous functions on an ellipse.