[Merged by Bors] - feat(analysis/special_functions/pow): smoothness of complex.cpow
#6447
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* `x ^ y` is smooth in both variables at `(x, y)`, if `0 < re x` or `im x ≠ 0`; * `x ^ y` is smooth in `y` if `x ≠ 0` or `y ≠ 0`.
sgouezel
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Feb 27, 2021
Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr>
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…6447) * `x ^ y` is smooth in both variables at `(x, y)`, if `0 < re x` or `im x ≠ 0`; * `x ^ y` is smooth in `y` if `x ≠ 0` or `y ≠ 0`.
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…6447) * `x ^ y` is smooth in both variables at `(x, y)`, if `0 < re x` or `im x ≠ 0`; * `x ^ y` is smooth in `y` if `x ≠ 0` or `y ≠ 0`.
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x ^ yis smooth in both variables at(x, y), if0 < re xorim x ≠ 0;x ^ yis smooth inyifx ≠ 0ory ≠ 0.I'm not sure that we should use
0 < re x ∨ im x ≠ 0as an assumptionor switch to
¬(re x ≤ 0 ∧ im x = 0). Same question aboutx ≠ 0 ∨ y ≠ 0vs¬(x = 0 ∧ y = 0).