Theorems · Definition · complex analysis
Real.sinh
ℝ → ℝ
The real hyperbolic sine function, defined as the real part of the complex hyperbolic sine
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 142 results in Mathlib
- Foundations
- Depth 143 from the axioms, rests on 3,708 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Complex.ofRealproof · cited by 1,654
- Complex.reproof · cited by 882
- Complex.sinhproof · cited by 113
Cited by143
Results whose statement or proof uses this declaration.
- Complex.ofReal_sinhstatement · cited by 12
- Real.contDiff_sinhstatement · cited by 10
- Real.sinh_zerostatement · cited by 10
- Real.hasDerivAt_sinhstatement · cited by 8
- Real.sinh_arsinhstatement · cited by 8
- Real.hasDerivAt_coshstatement · cited by 7
- UpperHalfPlane.sinh_half_diststatement and proof · cited by 6
- Real.tanh_eq_sinh_div_coshstatement and proof · cited by 5
- Real.sinhEquivproof · cited by 5
- UpperHalfPlane.cmp_dist_eq_cmp_dist_coe_centerstatement and proof · cited by 5
- Real.sinh_eqstatement and proof · cited by 5
- Real.sinh_le_sinhstatement · cited by 5