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Epi/hypo convergence of finite-valued bivariate functions defined on the product of two subsets, with some connections to lopsided convergence, is considered. Namely, we deal with three full characterizations of this convergence: by epi/hypo convergence of the corresponding proper bifunctions, by explicit formulae of the lower and upper members of the intervals of the limits, and by the bicontinuity of the partial Legendre-Fenchel transform (i.e., the (extended) epi/hypo convergence of bifunctions is characterized by the epi-convergence of their convex parents). We emphasize that epi/hypo limits are not unique and form an entire equivalence class.

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