Suppose in the now respectable-looking conjectures K(-(t^(1/4)-1/t^(1/4))^2/4)==t^(1/4) K(1-t), 2 E(-(t^(1/4)-1/t^(1/4))^2/4)==t^(1/4) K(1-t)+E(1-t)/t^(1/4), we replace t by t^4 and then foolishly PowerExpand (t^4)^(1/4) -> t, 1/(t^4)^(1/4) -> 1/t: K(-(t-1/t)^2/4)==t K(1-t^4), 2 E(-(t-1/t)^2/4)==t K(1-t^4)+E(1-t^4)/t . Our identities now hold only in the wedge -π/4 < arg(t) ≤ π/4. But it seems that whenever we have an identity so restricted, simply replacing t by t^(1/4) extends validity back to -π < arg(t) ≤ π, i.e., the whole plane. And indeed this substitution recovers our general identity, undoing our reckless PowerExpand. Puzzle: Suppose we only semifoolishly replace (t^4)^(1/4) -> (t^2)^(1/2), 1/(t^4)^(1/4) -> 1/(t^2)^(1/2). That should work in half the plane. Which half? --rwg