Theorems · Definition · complex analysis
circleIntegral
{E : Type u_1} → [inst : NormedAddCommGroup E] → [NormedSpace ℂ E] → (ℂ → E) → ℂ → ℝ → EDefinition for $\oint_{|z-c|=R} f(z)\,dz$
- Cited by
- 60 results in Mathlib
- Foundations
- Depth 251 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Complexstatement and proof · cited by 5,565
- Real.piproof · cited by 1,774
- MeasureTheory.MeasureSpace.volumeproof · cited by 1,323
- derivproof · cited by 676
- intervalIntegralproof · cited by 546
- circleMapproof · cited by 117
Cited by62
Results whose statement or proof uses this declaration.
- cauchyPowerSeriesproof · cited by 13
- Complex.cderivproof · cited by 10
- circleIntegral.integral_congrstatement · cited by 4
- circleIntegral.integral_substatement · cited by 4
- Complex.two_pi_I_inv_smul_circleIntegral_sub_inv_smul_of_differentiable_on_off_countablestatement and proof · cited by 3
- Complex.circleIntegral_sub_inv_smul_of_differentiable_on_off_countablestatement and proof · cited by 3
- circleIntegral.integral_radius_zerostatement · cited by 3
- circleIntegral.integral_smul_conststatement · cited by 3
- circleIntegral.norm_integral_le_of_norm_le_conststatement · cited by 3
- DiffContOnCl.circleIntegral_one_div_sub_center_pow_smulstatement · cited by 3
- Complex.circleIntegral_one_div_sub_center_pow_smul_of_differentiable_on_off_countablestatement and proof · cited by 2
- Complex.circleIntegral_sub_center_inv_smul_eq_of_differentiable_on_annulus_off_countablestatement · cited by 2