Radial basis functions, constructed from Slater type r(n*-1)e(-zeta r). and generalized exponential type r(n*-1)e(-zeta r mu) functions with the generalized hyperbolic cosine type functions cosh(pq)(beta r) and cosh(pq)(beta r(mu)), where p and q are arbitrary parameters, are proposed and applied to Hartree-Fock-Roothaan calculations of atomic systems. The performance of new basis functions within the minimal basis sets framework has been compared to numerical Hartree-Fock results and previous results presented by similar basis functions in the literature. The results obtained by the new basis sets surpass the accuracy of existing basis sets of similar hyperbolic cosine type functions. (C) 2015 Elsevier B.V. All rights reserved.