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We give an integral representation for the Kajihara's q-hypergeometric series W^M, 2. And we construct a q-difference system that corresponds to this integral. This system is an extension of the variant of q-hypergeometric equation of degree three, defined by Hatano-Matsunawa-Sato-Takemura. We show that this system includes the q-Appell-Lauricella system as a degeneration.
Takahiko Nobukawa (Thu,) studied this question.