Theorems · Theorem · complex analysis
Complex.cpow_natCast
∀ (x : ℂ) (n : ℕ), x ^ ↑n = x ^ n
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Complexstatement and proof · cited by 5,565
- mul_oneproof · cited by 3,885
- Complex.cpow_oneproof · cited by 20
- Complex.cpow_nat_mulproof · cited by 4
Cited by12
Results whose statement or proof uses this declaration.
- zeta_nat_eq_tsum_of_gt_oneproof · cited by 4
- two_mul_riemannZeta_eq_tsum_int_inv_pow_of_evenproof · cited by 2
- Complex.tendsto_one_add_pow_exp_of_tendstoproof · cited by 1
- HurwitzZeta.sinZeta_two_mul_nat_add_oneproof · cited by 1
- HurwitzZeta.sinZeta_two_mul_nat_add_one'proof · cited by 1
- Complex.cpow_ofNatproof · cited by 1
- HurwitzZeta.cosZeta_two_mul_natproof · cited by 1
- HurwitzZeta.cosZeta_two_mul_nat'proof · cited by 1
- Complex.GammaSeq_eq_approx_Gamma_integralproof · cited by 1
- Complex.one_div_one_sub_pow_hasFPowerSeriesOnBall_zeroproof · cited by 1
- Complex.tendsto_one_add_div_pow_expproof · cited by 0
- Complex.IsExpCmpFilter.isLittleO_pow_mul_expproof · cited by 0