Theorems · Theorem · complex analysis
Complex.tan_mul_I
∀ (x : ℂ), Complex.tan (x * Complex.I) = Complex.tanh x * Complex.I
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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.cosproof · cited by 279
- Complex.coshproof · cited by 118
- Complex.sinhproof · cited by 113
- Complex.tanstatement · cited by 77
- mul_div_right_commproof · cited by 20
- Complex.tanhstatement and proof · cited by 20
- Complex.cos_mul_Iproof · cited by 6
- Complex.sin_mul_Iproof · cited by 5
- Complex.tanh_eq_sinh_div_coshproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Complex.tan_add_mul_Iproof · cited by 1