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