We prove a necessary and sufficient condition for the integrability of the weight associated to the exceptional Laguerre polynomials. This condition is very much related to the fact that the associated second order differential operator has no singularities in (0, +∞).2010 Mathematics Subject Classification. 42C05, 33C45, 33E30.

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Let J denote the Bessel function of order . The functions y␣ r2y␤ r2y1r2 Ž 1r 2 .x J x , n s 0, 1, 2, . . . , form an orthogonal system in ␣q␤q2 nq1. In this paper we analyze the range of p, ␣ , and ␤ for which the Fourier series with respect to this system converges in the p ŽŽ . ␣ . L 0, ϱ , x dx -norm. Also, we describe the space in which the span of the system is dense and we show some of its properties. Finally, we study the almost everywhere convergence of the Fourier series for functions in such spaces. ᮊ Academic Press

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