Generalized p-adic hypergeometric functions of logarithmic type are introduced, shown to obey congruence relations like prior work, and proven to have zero special values at t=1 under certain conditions.
Dwork, p-adic cycles, Publications mathematiques de IHES, tome37
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On special values of generalized $p$-adic hypergeometric functions of logarithmic type
Generalized p-adic hypergeometric functions of logarithmic type are introduced, shown to obey congruence relations like prior work, and proven to have zero special values at t=1 under certain conditions.