On the Convergence of the Linear Means of Jacobi Series at Lebesgue Points in the Case of Half-Integer $\alpha$

We investigate the convergence of the linear means of the Fourier–Jacobi series of functions $f(x)$ from the weight space $L_{\alpha,\beta}[-1,1]$ for $x=1$ for the case in which this point is a Lebesgue point for $f$. We establish sufficient summability conditions depending on the behavior of the function on the closed interval $[-1,0]$ and on the properties of the matrix involved in the summation method.