We investigate the spectral properties of one-dimensional lattices with position-dependent hopping amplitudes and on-site potentials that are smooth bounded functions of the position. We find an exact integral form for the density of states (DOS) in the limit of an infinite number of sites. which we derive using a mixed Bloch-Wannier basis consisting of piecewise Wannier functions. Next. https://parisnaturalfoodes.shop/product-category/hair-formula/