On linear combinations of L-orthogonal polynomials associated with distributions belonging to symmetric classes

This paper deals with the classes S 3 ( ω , β , b ) of strong distribution functions defined on the interval [ β 2 / b , b ] , 0 < β < b ⩽ ∞ , where 2 ω ∈ Z . The classification is such that the distribution function ψ ∈ S 3 ( ω , β , b ) has a (reciprocal) symmetry, depending on ω , about the point β . We consider properties of the L-orthogonal polynomials associated with ψ ∈ S 3 ( ω , β , b ) . Through linear combination of these polynomials we relate them to the L-orthogonal polynomials associated with some φ ∈ S 3 ( 1 / 2 , β , b ) .