Let R(a,b)n=P(a,b)n/P(a,b)n(1) be the normalised Jacobi polynomials. For α≥0, put ξ0=−1 and let ξn be the largest zero of R(α+1,α)n for n≥1. We prove that

for every k≥1. This determines the pointwise lower envelope of the normalised ultraspherical polynomials and answers Question 2 posed by F. M. de Oliveira Filho in his 2009 thesis.