This would be like how log1p(z) is more relatively accurate for small argument than log(1+z). The use of 1m makes sense here with respect to the branch cut.
Then, evaluating an elliptic integral near unity, such as K(1-1/α^2) for large α could be converted to a call to some K1m(1/α^2) that calls the appropriate _₂F₁1m.