A Jenkins–Serrin problem on the strip

We describe the family of minimal graphs on strips with boundary values ±∞±∞ disposed alternately on edges of length 1, and whose conjugate graphs are contained in horizontal slabs of width 1 in R3R3. We can obtain as limits of such graphs the helicoid, all the doubly periodic Scherk minimal surfaces and the singly periodic Scherk minimal surface of angle π/2π/2.