Transformation from the Mittag-Leffler expansion to the expansion of the potential of an arbitrary body in the region of its analyticity

A transformation is found between the function 1/(1 - z) of a complex variable, defined a two-dimensional stellar region, to the reciprocal distance $1/\Delta$ that is a function of a real variable defined in three-dimensional space. Formulas relating the coefficients of the expansion of $1/\Delta$ in terms of spherical functions with the coefficients of the Mittag-Leffler expansion of the corresponding complex function 1/(l - z) are derived.