Theorems · Theorem · complex analysis
Complex.mul_cpow_ofReal_nonneg
∀ {a b : ℝ}, 0 ≤ a → 0 ≤ b → ∀ (r : ℂ), (↑a * ↑b) ^ r = ↑a ^ r * ↑b ^ r- Cited by
- 12 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- mul_oneproof · cited by 3,885
- MulZeroClass.mul_zeroproof · cited by 2,091
- Complex.ofRealstatement and proof · cited by 1,654
- MulZeroClass.zero_mulproof · cited by 1,625
- LT.lt.ne'proof · cited by 1,417
- eq_or_neproof · cited by 1,117
- Complex.expproof · cited by 612
- add_mulproof · cited by 363
- Complex.logproof · cited by 187
- mul_ne_zeroproof · cited by 178
Cited by12
Results whose statement or proof uses this declaration.
- Complex.integral_cpow_mul_exp_neg_mul_Ioiproof · cited by 2
- Complex.betaIntegral_scaledproof · cited by 1
- mellin_comp_mul_leftproof · cited by 1
- Real.tendsto_integral_gaussian_smul'proof · cited by 1
- ZMod.LFunction_eq_LSeriesproof · cited by 1
- Complex.Gammaℝ_mul_Gammaℝ_add_oneproof · cited by 1
- Complex.GammaSeq_eq_approx_Gamma_integralproof · cited by 1
- Complex.natCast_mul_natCast_cpowproof · cited by 1
- hasSum_mellinproof · cited by 1
- hasSum_mellin_pi_mulproof · cited by 1
- Complex.div_cpow_ofReal_nonnegproof · cited by 0
- MellinConvergent.comp_mul_leftproof · cited by 0