Theorems · Theorem · special functions
norm_cexp_neg_mul_sq
∀ (b : ℂ) (x : ℝ), ‖Complex.exp (-b * ↑x ^ 2)‖ = Real.exp (-b.re * x ^ 2)
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Norm.normstatement · cited by 5,413
- mul_commproof · cited by 2,262
- Complex.ofRealstatement and proof · cited by 1,654
- Complex.restatement and proof · cited by 882
- Real.expstatement and proof · cited by 871
- Complex.expstatement · cited by 612
- Complex.ofReal_powproof · cited by 81
- Complex.norm_expproof · cited by 33
- Complex.re_ofReal_mulproof · cited by 20
- Complex.neg_reproof · cited by 16
Cited by4
Results whose statement or proof uses this declaration.
- integrable_cexp_neg_mul_sqproof · cited by 2
- integral_mul_cexp_neg_mul_sqproof · cited by 1
- integrable_mul_cexp_neg_mul_sqproof · cited by 1
- continuousAt_gaussian_integralproof · cited by 1