Pijeira Cabrera, Héctor EstebanRivero Castillo, Daniel Alberto2022-01-252022-01-252020-05Pijeira-Cabrera, H. & Rivero-Castillo, D. (2019). Iterated Integrals of Jacobi Polynomials. Bulletin of the Malaysian Mathematical Sciences Society, 43(3), 2745–2756.0126-6705https://hdl.handle.net/10016/33954Let 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.12eng© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2019.Asymptotic behaviorIterated integralsJacobi polynomialsZeros of polynomialsresearch articleMatemáticashttps://doi.org/10.1007/s40840-019-00831-8open access274532756Bulletin of the Malaysian Mathematical Sciences Society43AR/0000025730