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In this paper, we give a Thomae type formula for  K 3 surfaces  X  given by double covers of the projective plane branching along six lines. This formula gives relations between theta constants on the bounded symmetric domain of type I 22  and period integrals of  X . Moreover, we express the period integrals by using the hypergeometric function  F   S   of four variables. As applications of our main theorem, we define ℝ 4 -valued sequences by mean iterations of four terms, and express their common limits by the hypergeometric function  F   S  .

Thomae type formula for K 3 surfaces given by double covers of the projective plane branching along six lines