The convergence of sequences of Legendre Pad6 approximants to scattering amplitudes arising in potential scattering is discussed. It is shown that if the amplitude for scattering by the Coulomb potential or the absorptive part of a scattering amplitude whose double spectral function obeys a certain bound are suitably modified, convergent sequences of Legendre Pad6 approximants may be constructed. Numerical results are presented for the Coulomb scattering amplitude. Common A K and Stacey T 1978 J. Phys. A : Math. Gen. 11 259-73 Gradshteyn I S and and Ryzhik I M 1965 Tables of Integrals, Series and Products (New York: Academic) Kinoshita T, Loeffel J J and Martin A 1964 Phys. Rev. B 135 1464 Landau L D and Lifshitz E M 1958 Quantum Mechanics (Oxford: Pergamon Press) Nuttall J 1976 University of London, Ontario Preprint Taylor J R 1974 Nuovo Cim. B 23 313 Yennie D R, Ravenhall D G and Wilson R N 1954 Phys. Rev. 95 500