  The Slater-type orbital basis with non-integer principal quantum numbers is a
physically and mathematically motivated choice for molecular electronic
structure calculations in both non-relativistic and relativistic theory. The
non-analyticity of these orbitals at $r=0$, however, requires analytical
relations for multi-center integrals to be derived. This is nearly
insurmountable. Previous papers by present authors eliminated this difficulty.
Highly accurate results can be achieved by the procedure described in these
papers, which place no restrictions on quantum numbers in all ranges of orbital
parameters. The purpose of this work is to investigate computational aspects of
the formulae given in the previous paper. It is to present a method which helps
to increase computational efficiency. In terms of the processing time,
evaluation of integrals over Slater-type orbitals with non-integer principal
quantum numbers are competitive with those over Slater-type orbitals with
integer principal quantum numbers.
