Theorems · Theorem · complex analysis
Complex.exp_sum
∀ {α : Type u_1} (s : Finset α) (f : α → ℂ), Complex.exp (∑ x ∈ s, f x) = ∏ x ∈ s, Complex.exp (f x)- Defined in
- Mathlib.Analysis.Complex.Exponential
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 146 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Complexstatement and proof · cited by 5,565
- Finset.sumstatement · cited by 5,195
- Finset.prodstatement · cited by 2,356
- Complex.expstatement · cited by 612
- map_prodproof · cited by 108
- Complex.expMonoidHomproof · cited by 5
Cited by8
Results whose statement or proof uses this declaration.
- ProbabilityTheory.iIndepFun.hasGaussianLawproof · cited by 3
- ProbabilityTheory.charFun_stdGaussianproof · cited by 2
- HasSum.cexpproof · cited by 2
- MeasureTheory.charFun_piproof · cited by 2
- MeasureTheory.charFunDual_piproof · cited by 1
- GaussianFourier.integrable_cexp_neg_sum_mul_addproof · cited by 1
- hasProdUniformlyOn_of_clogproof · cited by 1
- GaussianFourier.integral_cexp_neg_sum_mul_addproof · cited by 1