On some multiple series which include the real analytic Eisenstein series

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Our main achievement of the present project is to establish a transformation formula of some Barnes' type double Eisenstein series. We obtained a asymptotic expansion and various explicit formulas of the specific value of these Eisenstein series. The double analog of the Lipschits formula via the Mellin-Barnes integral transformation is the key ingredient in our proof.We also derived a transformation formula for a certain kind of Eisenstein series occurs in aerodynamic interference calculations, which provides extensive understanding of some double series in wind-tunnel wall corrections.