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We introduce new p-adic convergent functions, which we call the p-adichypergeometric functions of logarithmic type. The first main result is to provethe congruence relations that are similar to Dwork's. The second main result isthat the special values of our new functions appear in the syntomic regulatorsfor hypergeometric curves, Fermat curves and some elliptic curves. According tothe p-adic Beilinson conjecture by Perrin-Riou, they are expected to be relatedwith the special values of p-adic L-functions. We provide one example for this.

New p-adic hypergeometric functions and syntomic regulators