Mellin–Barnes representation for $SL(2, \mathbb{C})$ magnet

We consider $SL(2, \mathbb{C})$ spin magnet and construct eigenfunctions for the element $A(u)$ of the monodromy matrix. We use recursive procedure which gives representations of these functions in the form of Mellin-Barnes type integrals. We compare these functions to those constructed earlier by S. Derkachov and A. Manashov (Gauss–Givental representation) and prove that they coincide up to normalization factor.