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An approximate expression for the Pauli kinetic energy functional Tp is advanced in terms of the Liu‐Parr expansion [S. Liu, R.G. Parr, Phys. Rev. A1997, 55, 1792] which involves a power series of the one‐electron density. We use this explicit functional for Tp to compute the value of the noninteracting kinetic energy functional Ts of 34 atoms, from Li to Kr (and their positive and negative monoions)...