Expansions and Characterizations of Sieved Random Walk Polynomials

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2023
• 1. Verfasser: Kahler, Stefan
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2023
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/212028
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: Expansions and Characterizations of Sieved Random Walk Polynomials. Stefan Kahler. SIGMA 19 (2023), 103, 18 pages

We consider random walk polynomial sequences (ₙ())ₙ∈ℕ₀ ⊆ ℝ[] given by recurrence relations ₀() = 1, ₁() = , ₙ() = (1−cₙ)ₙ₊₁()+cₙₙ₋₁(), ∈ ℕ with (cₙ)ₙ∈ℕ ⊆ (0, 1). For every ∈ ℕ, the -sieved polynomials (ₙ(; ))ₙ∈ℕ₀ arise from the recurrence coefficients c(; ):= cₙ/ₖ if | and c(; ):= 1/2 otherwise. A...