Let a is-an-element-of Z+ and f is-an-element-of L(p)(R+), 1 less-than-or-equal-to p less-than-or-equal-to infinity. Denote by c(j) the inner product of f and the Laguerre function L(j)a. We prove that if {c(j)} satisfies [GRAPHICS] for some k is-an-element-of N, then the Laguerre series SIGMA c(j)L(j)a converges to f almost everywhere.
