Theorems · Theorem · complex analysis
Complex.two_sin
∀ (x : ℂ), 2 * Complex.sin x = (Complex.exp (-x * Complex.I) - Complex.exp (x * Complex.I)) * Complex.I
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 143 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Complex.Istatement and proof · cited by 866
- Complex.expstatement and proof · cited by 612
- Complex.sinstatement · cited by 258
- two_ne_zeroproof · cited by 251
- mul_div_cancel₀proof · cited by 77
Cited by2
Results whose statement or proof uses this declaration.
- Complex.sinh_mul_Iproof · cited by 10
- Complex.norm_exp_I_mul_ofReal_sub_oneproof · cited by 1