  A Lemma of Riemann--Lebesgue type for Fourier--Jacobi coefficients is
derived. Via integral representations of Dirichlet--Mehler type for Jacobi
polynomials its proof directly reduces to the classical Riemann--Lebesgue Lemma
for Fourier coefficients. Other proofs are sketched. Analogous results are also
derived for Laguerre expansions and for Jacobi transforms.
