Abstract
For the class of generalised Hulthen s-wave potentials VGH(p)(r)= Sigma i=1p giai exp(- gamma ir)/(1- Sigma j=1p aj exp(- gamma jr), p>or=1, the exact solution is presented for both the Schrodinger and Klein-Gordon equations. This simultaneous solubility represents a new non-perturbative treatment of the kinematical relativistic corrections and is based on a non-standard generalisation of the hypergeometric function.