Exact formulas and their evaluation for Slater-type-orbital overlap integrals with large quantum numbers

Using the Löwdin α-function method with a computer-generated C-matrix associated with a displaced Slater-type orbital, an exact closed formula as well as a Taylor series with exact coefficients is produced for the overlap integral over two 7gγ orbitals. It is shown how ten-decimal-digit accuracy is achieved throughout the entire range of parameter values. A noteworthy development is the great simplification of this overlap formula made possible by factoring out (1-t${)}^{20}$ by means of computer algebra.