Left panel: principal jump corrections of the stream function Ψ induced by the presence of a source of strength m (gray circle) located at r_k. The use of the single-argument arctan (4) for the definition of Ψ entrails jumps by ± πm (shown in red) when crossing the vertical line x = x_k either “above” (y > y_k) or “below” (y < y_k) the source, while in the case of definition (17), only a single jump by ± 2πm (shown in blue) occurs across the horizontal line y = y_k, x < x_k to the “left” of the source. Right panel: sample stream lines for three stellar wind sources with equal strengths m₁ = m₂ = m₃ = 1 (black circle) computed from curves of constant stream function Ψ(x, y) as given in Eq. (17) with jump corrections according to Eq. (24). Colors indicate the various values of Ψ. The two stream lines emanating from the right source at r₃ = (1, 0) are both singled valued because there is no other source to its right, while the stream line pointing into the − y direction from the central source at r₂ = (0, 1) has a jump of − π at y = y₃ = 0. Finally, the source at r₁ = (−1, 0) has jumps of ± π in both the upward- and downward-pointing stream line at y = y₂ = 1 and y = y₃ = 0, respectively.