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.
This would be like how
log1p(z)is more relatively accurate for small argument thanlog(1+z). The use of1mmakes sense here with respect to the branch cut.Then, evaluating an elliptic integral near unity, such as
K(1-1/α^2)for largeαcould be converted to a call to someK1m(1/α^2)that calls the appropriate_₂F₁1m.