<p>As a generalization of the classical knots, knotoids are equivalence classes of immersions of the oriented unit interval in a surface. In recent years, a variety of invariants of spherical and planar knotoids have been constructed as extensions of invariants of classical and virtual knots. In this paper, we introduce a three-variable transcendental invariant of planar knotoids which is defined over an index function of a Gauss diagram. We describe properties of this invariant and show that it is a Vassiliev invariant of order one. We also discuss the Gordian distance between planar knotoids and provide lower bounds on the Gordian distance of homotopic planar knotoids using the transcendental invariant.</p>