Equiconvergence of two Fourier series (Q1890561)

The authoress considers the generalized Jacobi polynomials \(\{Q_n(x): n= 0, 1,\dots; x\in [- 1, 1]\}\), which are orthonormal with respect to the weight function \[ w(x):= (1- x)^\alpha(1+ x)^\beta \exp[u(x)],\quad \alpha, \beta> -1, \] where \(u(x)\) is a real function satisfying some general conditions. She studies the Fourier expansion with respect to \(\{Q_n(x)\}\) of a function \(f\) such that the integral \(\int^{\pi/2}_{-\pi/2} f(\sin t) dt\) exists, and proves a comparison theorem on the equiconvergence of this expansion with an associated trigonometric Fourier series (in the case where \(\alpha, \beta> -1/2\)).