Theorems · Theorem · real analysis
Complex.ofReal_cpow_of_nonpos
∀ {x : ℝ}, x ≤ 0 → ∀ (y : ℂ), ↑x ^ y = (-↑x) ^ y * Complex.exp (↑Real.pi * Complex.I * y)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites32
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Norm.normproof · cited by 5,413
- mul_oneproof · cited by 3,885
- add_zeroproof · cited by 2,707
- MulZeroClass.mul_zeroproof · cited by 2,091
- Real.pistatement and proof · cited by 1,774
- Complex.ofRealstatement and proof · cited by 1,654
- MulZeroClass.zero_mulproof · cited by 1,625
- eq_or_neproof · cited by 1,117
- Real.logproof · cited by 939
- LT.lt.neproof · cited by 872
Cited by4
Results whose statement or proof uses this declaration.
- intervalIntegral.intervalIntegrable_cpow'proof · cited by 7
- intervalIntegral.intervalIntegrable_cpowproof · cited by 2
- hasDerivAt_ofReal_cpow_const'proof · cited by 2
- Complex.continuousAt_ofReal_cpowproof · cited by 1