On the convergence of the linear means of Jacobi series at Lebesgue points in the case of half-integer α

We investigate the convergence of the linear means of the Fourier-Jacobi series of functions ?(x) from the weight space L _α,β for x = 1 for the case in which this point is a Lebesgue point for ?. We establish su.cient 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.