Alternative Orthogonal Rational Functions on a Half Line

Abstract

System of alternatively orthogonalized rational functions of Jacobi type on the half line [1, ∞) is defined and its properties are established. Three subsystems of proper and mixed systems of rational functions with nice properties are presented.

Curvilinearity and Orthogonality

“…Specific examples of orthogonal rational functions on the semi-axis were given in [1,9,14]. Alternative orthogonal rational functions on a half-line which provide term-byterm increasing rate of decay at infinity were introduced in [7].…”