  The integral representation of the two-parameter Mittag-Leffler function
$E_{\rho,\mu}(z)$ is considered in the paper that expresses its value in terms
of the contour integral. For this integral representation, the transition is
made from integration over a complex variable to integration over real
variables. It is shown that as a result of such a transition, the integral
representation of the function $E_{\rho,\mu}(z)$ has two forms: the
representation ``A'' and ``B''. Each of these representations has its
advantages and drawbacks. In the paper, the corresponding theorems are
formulated and proved, and the advantages and disadvantages of each of the
obtained representations are discussed.
