Theorems · Theorem · complex analysis
Complex.two_sinh
∀ (x : ℂ), 2 * Complex.sinh x = Complex.exp x - Complex.exp (-x)
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 5 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.
Cites5
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.expstatement and proof · cited by 612
- two_ne_zeroproof · cited by 251
- Complex.sinhstatement · cited by 113
- mul_div_cancel₀proof · cited by 77
Cited by5
Results whose statement or proof uses this declaration.
- Complex.sinh_mul_Iproof · cited by 10
- Complex.cosh_addproof · cited by 6
- Complex.sinh_addproof · cited by 6
- Complex.cosh_add_sinhproof · cited by 5
- Complex.cosh_sub_sinhproof · cited by 4