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We prove the failure of a.e. convergence of the Fourier expansion in terms of the orthonormal polynomials with respect to the measure (1 - x)α(1 + x)βdx + Mδ1 + Nδ1, where δt is the delta function at a point t and M > 0; N > 0: Lebesgue norms of Koornwinder's Jacobi-type polynomials are applied to obtain a new proof of necessary conditions for mean convergence. .

On convergence and divergence of Fourier expansions associated to Jacobi measure with mass points