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In this paper we continue investigation of the hypergeometric function${}_4F_3(1)$ as the function of its seven parameters. We deduce severalreduction formulas for this function under additional conditions that one ofthe top parameters exceeds one of the bottom parameters by a positive integeror reversely one of the bottom parameters exceeds one of the top parameters bya positive integer or both. We show that all such cases reduce to the case ofthe unit parameter difference. The latter case, in turn, can be expressed interms of certain linear combination of two series involving the logarithmicderivative of the gamma function.

Hypergeometric ${}_4F_3(1)$ with integral parameter differences