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On Polynomials Orthogonal with Respect to an Inner Product Involving Higher-Order Differences: The Meixner Case
2022
Mathematics
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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
doi:10.3390/math10111952
fatcat:jnmge2ss2vdnzl4hsvd5fw2vd4