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Theorems · Definition · complex analysis

circleIntegral

{E : Type u_1} → [inst : NormedAddCommGroup E] → [NormedSpace ℂ E] → (ℂ → E) → ℂ → ℝ → E

Definition for $\oint_{|z-c|=R} f(z)\,dz$

Defined in
Mathlib.MeasureTheory.Integral.CircleIntegral
Cited by
60 results in Mathlib
Foundations
Depth 251 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedAddCommGroupNormedSpace

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

cauchyPowerSeries · cited by 13cauchyPowerSeriesComplex.cderiv · cited by 10Complex.cderivcircleIntegral.integral_congr · cited by 4circleIntegral.integral_c…circleIntegral.integral_sub · cited by 4circleIntegral.integral_s…Complex.two_pi_I_inv_smul_circleIntegral_sub_inv_smul_of_differentiable_on_off_countable · cited by 3Complex.two_pi_I_inv_smul…Complex.circleIntegral_sub_inv_smul_of_differentiable_on_off_countable · cited by 3Complex.circleIntegral_su…circleIntegral.integral_radius_zero · cited by 3circleIntegral.integral_r…circleIntegral.integral_smul_const · cited by 3circleIntegral.integral_s…circleIntegral.norm_integral_le_of_norm_le_const · cited by 3circleIntegral.norm_integ…DiffContOnCl.circleIntegral_one_div_sub_center_pow_smul · cited by 3DiffContOnCl.circleIntegr…Complex.circleIntegral_one_div_sub_center_pow_smul_of_differentiable_on_off_countable · cited by 2Complex.circleIntegral_on…Complex.circleIntegral_sub_center_inv_smul_eq_of_differentiable_on_annulus_off_countable · cited by 2Complex.circleIntegral_su…Complex.circleIntegral_eq_zero_of_differentiable_on_off_countable · cited by 2Complex.circleIntegral_eq…circleAverage_sub_sub_inv_smul_of_differentiable_on_off_countable · cited by 2circleAverage_sub_sub_inv…circleIntegral.integral_eq_zero_of_hasDerivWithinAt' · cited by 2circleIntegral.integral_e…Real · cited by 25697RealNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceComplex · cited by 5565ComplexReal.pi · cited by 1774Real.piMeasureTheory.MeasureSpace.volume · cited by 1323MeasureSpace.volumederiv · cited by 676derivintervalIntegral · cited by 546intervalIntegralcircleMap · cited by 117circleMapcircleIntegralCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by62

Results whose statement or proof uses this declaration.