Uniform asymptotics for second-kind ultraspherical polynomials on the unit circle (Q1281678)

For the ultraspherical weight on the unit circle, \[ w_\gamma(\theta)= \text{const } |\sin \theta|^{2 \gamma}, \quad \theta \in [-\pi, \pi) , \] the orthogonal polynomials of the second kind are considered. The author finds uniform asymptotic expressions for this sequence (in terms of the polynomials of the first kind), valid in the closed unit disk, as well as two-sided bounds on the unit circle. In the proof, explicit expressions for the coefficients of the orthogonal polynomials of the first kind, obtained by \textit{V. M. Badkov} [Trudy Mat. Inst. Steklova 164, 3-36 (1983; Zbl 0583.42014)], are used.