The third virial coefficient ind(=2, 3) dimensions and its asymptote

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Abstract
The two-dimensional third virial coefficient is recalculated because of an error found in the calculation of the previous workers. Since the method of calculation of the two- and three-dimensional third virial coefficient is similar, both are calculated in a general manner following the method of Kihara. Asymptotic expressions are obtained for the expansion coefficient and the virial coefficient itself. A correction is made to Kihara's asymptotic formula for the expansion coefficient and his work is extended to the term of the next order. The calculation of the low temperature asymptote of the second virial coefficient is used to illustrate the method.