On special values of generalized $p$-adic hypergeometric functions of logarithmic type

Abstract

We introduce a new type of $p$-adic hypergeometric functions, which are generalizations of $p$-adic hypergeometric functions of logarithmic type defined by Asakura, and show that these functions satisfy the congruence relations similar to Asakura's. We also give numerical computations of the special values of these functions at $t=1$ and prove that these values are equal to zero under some conditions.