Thomae type formula for K3 surfaces given by double covers of the projective plane branching along six lines

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In this paper, we give Thomae type formula for surfaces 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 I₂₂ and period integrals of X. Moreover, we express the period integrals by using the hypergeometric function Fₛ of four variables. As an application of our main theorem, we define ⁴-valued sequences by mean iterations of four terms, and express their common limits by the hypergeometric function Fₛ.