ALTERNATIVE DERIVATIONS OF CERTAIN SUMMATION FORMULAS CONTIGUOUS TO DIXON'S SUMMATION THEOREM FOR A HYPERGEOMETRIC $_3F_2$ SERIES

ALTERNATIVE DERIVATIONS OF CERTAIN SUMMATION FORMULAS CONTIGUOUS TO DIXON'S SUMMATION THEOREM FOR A HYPERGEOMETRIC $_3F_2$ SERIES

In 1994, Lavoie et al. have obtained twenty tree interesting results closely related to the classical Dixon's theorem on the sum of a $_3F_2$ by making a systematic use of some known relations among contiguous functions. We aim at showing that these results can be derived by using the same technique developed by Bailey with the help of Gauss's summation theorem and generalized Kummer's theorem obtained by Lavoie et al..

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