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Abstract: In a previous paper an asymptotic expansion for lambda d in powers of 1-d wasdeveloped. The results of computer computations for some terms in theexpansion, as well as various quantities associated to the expansion, areherein presented. The computations in integer arithmetic are actually doneonly for d=1, d=2, and d=3, but some results for arbitrary dimension followfrom the general structure of the theory. In particular we obtain the next termin powers of 1-d, the 1-d^3 term in the asymptotic expansion for lambda d, aswell as checking the correctness of the terms previously calculated by hand.For d=2 and d=3 a second expansion for lambda d is defined and numericallystudied. Contrary to our hopes this second type of expansion appears not to beconvergent. There is not enough evidence to argue if the expansions forlambda d in powers of 1-d are convergent for either d=2 or d=3, but likely theyare not. Certainly convergence, but at a very slow rate, remains aninteresting possibility in all our cases.

Autor: Paul Federbush

Fuente: https://arxiv.org/

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