Polynomials orthogonal on the semicircle
The authors study the complex polynomials \(\{\pi_ n\}\) which are orthogonal with respect to the complex-valued inner product \((f,g)=\int^{\pi}_{0}f(e^{i\theta})g(e^{i\theta})d\theta.\) For these polynomials, they obtain a three-term recurrence relation, a linear differential equation of second order and discuss the nature of the zeros. A relationship between these polynomials and the Legendre polynomials is worked out. Finally, they discuss some interesting applications of these polynomials.
linear differential equation of second order
scientific article; zbMATH DE number 3975573
scientific article