Publication: Iterated integrals of Jacobi polynomials
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2020-05
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Springer Nature
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Abstract
Let P(α,β)n be the n-th monic Jacobi polynomial with α,β>−1. Given m numbers ω1,…,ωm∈C∖[−1,1], let Ωm=(ω1,…,ωm) and P(α,β)n,m,Ωm be the m-th iterated integral of (n+m)!n!P(α,β)n normalized by the conditions
dkP(α,β)n,m,Ωmdzk(ωm−k)=0, for k=0,1,…,m−1.
The main purpose of the paper is to study the algebraic and asymptotic properties of the sequence of monic polynomials {P(α,β)n,m,Ωm}n. In particular, we obtain the relative asymptotic for the ratio of the sequences {P(α,β)n,m,Ωm}n and {P(α,β)n}n. We prove that the zeros of these polynomials accumulate on a suitable ellipse.
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Asymptotic behavior, Iterated integrals, Jacobi polynomials, Zeros of polynomials
Bibliographic citation
Pijeira-Cabrera, H. & Rivero-Castillo, D. (2019). Iterated Integrals of Jacobi Polynomials. Bulletin of the Malaysian Mathematical Sciences Society, 43(3), 2745–2756.