On difference equations of Kravchuk-Sobolev type polynomials of higher order

2020/10/31 by Roberto S. Costas-Santos, Costas-Santos, Roberto S., Anier Soria-Lorente +1
Mathematics · Physics and Astronomy · #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Mathematical functions and polynomials #Nonlinear Waves and Solitons #math.CA

paper · pdf · doi:10.48550/arxiv.2011.00255

11 pages

arxiv created 2020/10/31 · openalex publication_date 2020/10/31 · arxiv updated 2020/11/03 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

In this contribution we consider sequences of monic polynomials orthogonal with respect to Sobolev-type inner product ⟨ f,g⟩ _λ,μ = ∑_x=0^Nf(x)g(x)\fracΓ(N+1) p^x(1-p)^N-x Γ(N-x+1) Γ(x+1) +λΔ^j f(0)Δ^j g(0)+μΔ^j f(N)Δ^j g(N), where 0<p <1, λ,μ∈ \mathbb R₊, n≤ N∈ \mathbb Z₊, j∈ \mathbb Z₊ and Δ denotes the forward difference operators. We derive an explicit representation for these polynomials. In addition, the ladder operators associated with these polynomials are obtained. As a consequence, the linear difference equations of second order are also given.

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