TY - EJOU
AU - Costas-Santos, Roberto S.
AU - Soria-Lorente, Anier
AU - Vilaire, Jean-Marie
TI - On Polynomials Orthogonal with Respect to an Inner Product Involving Higher-Order Differences: The Meixner Case
T2 - Mathematics
PY - 2022
VL - 10
IS - 11
SN - 2227-7390
AB - In this contribution we consider sequences of monic polynomials orthogonal with respect to the Sobolev-type inner product f,g=⟨uM,fg⟩+λTjf(α)Tjg(α), where uM is the Meixner linear operator, λ∈R+, j∈N, α≤0, and T is the forward difference operator Δ or the backward difference operator ∇. Moreover, we derive an explicit representation for these polynomials. The ladder operators associated with these polynomials are obtained, and the linear difference equation of the second order is also given. In addition, for these polynomials, we derive a (2j+3)-term recurrence relation. Finally, we find the Mehler–Heine type formula for the particular case α=0.
KW - Meixner polynomials
KW - Meixnerâ€“Sobolev orthogonal polynomials
KW - discrete kernel polynomials
DO - 10.3390/math10111952