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We investigate a relation between the Mordell-Tornheim type of multipleDirichlet series and a confluent hypergeometric function. We prove it byapplying the Mellin-Barnes integral formula. Also, main results in this papercontain two kinds of functional equations for double $L$-functions as a specialcase.

A relation between the Mordell-Tornheim multiple Dirichlet series and the confluent hypergeometric function