L-orthogonal polynomials associated with related measures

A positive measure ψ defined on [ a , b ] such that its moments μ n = ∫ a b t n d ψ ( t ) exist for n = 0 , ± 1 , ± 2 , …  , can be called a strong positive measure on [ a , b ] . When 0 ⩽ a < b ⩽ ∞ , the sequence of polynomials { Q n } defined by ∫ a b t − n + s Q n ( t ) d ψ ( t ) = 0 , s = 0 , 1 , … , n − 1 , exist and they are referred here as L-orthogonal polynomials. We look at the connection between two sequences of L-orthogonal polynomials { Q n ( 1 ) } and { Q n ( 0 ) } associated with two closely related strong positive measures ψ 1 and ψ 0 defined on [ a , b ] . To be precise, the measures are related to each other by ( t − κ ) d ψ 1 ( t ) = γ d ψ 0 ( t ) , where ( t − κ ) / γ is positive when t ∈ ( a , b ) . As applications of our study, numerical generation of new L-orthogonal polynomials and monotonicity properties of the zeros of a certain class of L-orthogonal polynomials are looked at.