Sixth-order term of the gradient expansion of the kinetic-energy density functional

A generalization of Hodges's method of obtaining the gradient expansion is derived and then employed to determine the sixth-order term. The formula for it is as follows: ${T}₆[{ρ}]={{(3{{π}}²)}^{{-}413}}{45360{∫}{{ρ}}^{{{-}1}{3}}[13{({{∇}{{∇}}²{ρ}}{{ρ}})}²+{2575}{144{({{{∇}}²{ρ}}{{ρ}})}³}+{249}{16{({{∇}{ρ}}{{ρ}})}²({{{∇}}⁴{ρ}}{{ρ}})}+{1499}{18{({{∇}{ρ}}{{ρ}})}²{({{{∇}}²{ρ}}{{ρ}})}²}{-}{1307}{36{({{∇}{ρ}}{{ρ}})}²({{{→}}{{∇}}{ρ}·{}{{→}}{{∇}}{{∇}}²{ρ}}{{{ρ}}²})}+{343}{18{({{{→}}{{∇}}{ρ}·{}{{→}}{{∇}}{{→}}{{∇}}{ρ}}{{{ρ}}²})}²+{8341}{72({{{∇}}²{ρ}}{{ρ}}){({{∇}{ρ}}{{ρ}})}⁴}{-}{1600495}{2592{({{∇}{ρ}}{{ρ}})}⁶}]{d}³r}}$. For atomic densities, ${T}₆[{ρ}]$ is divergent near the nucleus and at large distances.