Abstract :
Considered in this paper are two systems of polynomials that are orthogonal systems for two different but related inner product spaces. One of these systems is a special case (λ=12) of the symmetric Meixner–Pollaczek polynomial systems, Pn(λ)(x/2,π/2), and it turns out that this system is closely related to a system of orthogonal polynomials in the strip, S={z:−1<Im(z)<1}. Moreover, there are some simple operators that connect the systems with each other. We have designated the special case of the symmetric Meixner–Pollaczek polynomial systems by τ̃n and the latter system on the strip by σ̃n, and we have been able to show that this system is the limiting case of the symmetric Meixner–Pollaczek polynomial systems, Pn(λ)(x/2,π/2) as λ→0.
