Application of the Minimax Approximation to the Reduced Partition Function of Isotopic Molecules

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Abstract
The minimax approximation to the reduced partition function ratio of isotopic molecules is worked out. The applied approximation is an even power series in hν / kT which is convergent for all values of the argument. Its error function has as many extrema as possible and oscillates with uniform amplitudes of the smallest possible value. The rate of convergence and the utility of the minimax method are discussed through numerical calculations for various polyatomic molecules and the results are compared with those obtained by other approximations.